Considering that there will be 2 teams who will advance straight to the playoffs and one will move to the knockout phase, this European Championship group A is one of the evenest ones.
Italy is the main favourite, I'm sure, without even checking the odds. The rest of the teams should be all very close, Switzerland with the slightest edge.
Let's check the odds. Italy around 1.06 and other three teams all between 1.5 to 1.8. 

Games are played in Rome and Baku. So Italy has already an advantage here. Let's dig deeper into teams.

European Championship Group A - Italy

Italy failed to qualify for the 2018 World Cup, and that says a lot. This team is hungry and should be well motivated to give 110%. They are placed in 7th to 8th place as an outright winner with odds around 12.
Their recent games have been consistent and beat teams like Poland, Netherlands, Bosnia and Herzegovina.
There's one concern for them. In the quarter-finals, they should meet Belgium, a top 3 candidate, to lift the trophy.
Italy sits in 7th place in the current FIFA rankings list and is coached by Roberto Mancini.

Potential squad

At first sight over the potential squad list, there's hard to spot a star, a world-class star. This is due to 2 reasons. Most of the squad will be from Serie A - Inter, Juventus, Roma, Napoli and Lazio. Only Roma is playing in at least the quarter-finals of bigger European competitions. I mean the Champions League and Europa League.

According to Transfermarkt, the average squad value is in the region of 730m. The most expensive players are all around the 50m mark - Gigi Donnarumma, Verratti, Barella and Chiesa.

Goalkeepers - Sirigu, Meret, Donnarumma and Cragno. Two of them are with 25 and 26 games while Meret and Cragno with only 1 game for the national team. Sirigu is more experienced for sure (34 years old) while Donnarumma has been a regular for AC Milan for years despite being only 22 years old. Very decent options in the goalkeeping department for Italy.

Defenders - The famous Bonucci and Chiellini partnership at this level is finished. These guys have been an actual definition of a defensive partnership on a world-class level before anyone knew the words crypto or Tesla. We saw these guys together in a win against the Netherlands (shows they still got it!), but I'm sure their legs can't handle these games in such a short period. Who will step up..Bastoni? Romagnoli? Acerbi? Mancini has used a lot of rotation in the defence, according to the opponent.
There are 5-6 candidates with at least ten games for the national team when excluding the legends. Ten games!

Midfielders - In the recent games squads, they had two midfielders with over ten games. 24 years old Barella and 24 years old Pellegrini. Jorginho (29) and Verratti (28) are the with 27 and 40 games. The first two are playing in Serie A while Jorginho in Chelsea and Verratti in PSG. No world-class player here as well. Nicolo Barella should be a focal point in this midfield and run the show. He lead the Inter to the Serie A Championship title this season.
Three players in the potential squad list lost their first Europa League game against Manu 6-2.
There's literally no one even close to Pirlo and De Rossi quality which carried the team for a long time.

Attackers - Immobile has been lethal in Serie A for Lazio for many seasons by now. 31 years old 12 goals in 45 games for Italy. Belotti has 11 goals in 32 games, and then there's also Insigne and Berardi (11 goals combined). Who from them would you name as a top 10 striker in the world at the moment? A top 15 striker?
There's one name that stands out for me, and it's Federico Chiesa. 23 years old winger who has 8 goals and 9 assists in Serie A this season. A breakout season and 8 goals is a big number in a team with Ronaldo, Morata and Dybala.

Overall expectation

A proper top 10 team in this competition at the moment. Have the necessary tools to walk out of the group stage. Some good potential young players could make a small storm and get the attention, but anything further from the quarter-finals is a big surprise in a European Championship Group A.

European Championship Group A - Turkey

Turkey sits in 13th position in UEFA rankings. Ahead of Croatia, Denmark, Switzerland, for example. They have had some good results under Senol Günes and has beat teams like the Netherlands, Norway, Russia and draws against Serbia and Germany. They are playing a nice attacking game with fast flow and goals, goals, goals. In 2016 Euros they were stopped in the group stage already. In the 2018 WC qualification tournament, there were a coaching change and a lot of internal issues to stop the team from reaching the final tournament.

Potential squad

The core of the team is an interesting one. Local league players from Turkey and mixed with some good players from top leagues like Premier League, Serie A and French League 1. Good base to get through from the European Championship Group A.

Their odds are similar compared to Switzerland to qualify from the group, and I think it's fair. Turkey should qualify from this group as 2nd or 3rd team.

The squad value according to Transfermarkt is around 200m and the most valued part of the team is defence.

Goalkeepers - The probable started in goal is Mert Günok from Basaksehir. Alternatives are also from the local league. So, not the strongest part of the team, but in Euros, there are not many teams with players from the top leagues only in every department.

Defenders - Some top talent in the defence! Caglar Söyüncü from Leicester and Ozan Kabak from Liverpool. Mert Müldür plays for Sassuolo in Italy Serie A and of course Merih Demiral from Juventus.
A solid base of players from the top leagues.

Midfielders - Again, a nice core consisting of players from the top leagues. Hakan Calhanoglu is the star from AC Milan and 13 goals for the national team. Okay Yokusly from West Brom, Yusuf Yazici have a solid season for Lille and fighting for the French League champions trophy. Cengiz Ünder also plays for Leicester and had some decent seasons for AS Roma.

Attackers - 35 years old Buruk Yilmaz have had a career season during the last 2years and earned a contract with Lille. Demolished the Netherlands in the qualifiers and have 28 goals for the national team. He is supported by Kenan Karaman from Düsseldorf and Enes Ünal from Getafe.
Last but not least, Cenk Tosun. A name that should be familiar for Premier League fans. 9 goals in Everton and currently loaned out to Besiktas.

Overall expectation

A strong candidate to get through the group stage for sure from European Championship Group A. Italy can be a headache for them. Switzerland and Wales should be equal opponents, and games could go either way. Important is that with the new coach, the team seems to have a new breath and a nice mixture of players from top leagues and experience with youth.

European Championship Group A - Switzerland

I don't know why, but this team always seems to underperform on the big stage for me. In the last WC Final tournament, they drew with Brazil, beat Serbia and drew with Costa Rica. Second place in the group and then lost against Sweden in the round of sixteen. In the last Euros, they were also eliminated in the round of sixteen. This time by Poland and penalty shootout.

In the FIFA ranking, they sit only in 29th place at the moment! Behind Cyprus, Ukraine, Denmark and Czech Republic. The team value is around 230m, and the current head coach is Vladimir Petkovic.

In recent games, they have beat Finland, Bulgaria and Lithuania.
They drew against Germany and Spain but lost against Ukraine and Croatia. A lot of mixed emotions for me as they have a very solid squad to pick from for the European Championship Group A.

Potential squad

They can have a full starting 11 based on players from the top leagues. There's one worry tough as all of them are not main players in their teams.  Many core players are at their peak age, so Switzerland has to work it out during these Euros to take something from this era. The current core played together with Stephan Lichtsteiner and Gökhan Inler, and the team needs to find substitutes for them for the European Championship Group A.

A lot of goals in the team based on stats and compared with other teams in the group, even with Italy!

Goalkeepers - Yann Sommer has been for some seasons now as one of the best between the sticks in Bundesliga. 60 games for the national team and other goalkeepers have 5 combined, so not worth digging deep here. Sommer will be the number 1. Top 5 goalkeeper in this tournament for me.

Defenders - Versatile winger Ricardo Rodriguez with 79 games and 8 goals. He has played in Germany and Italy for years and well known for his attacking capabilities and endless work rate.
Manuel Akanji and Nico Elvedi are both playing in German Bundesliga as main team players, starters. Both are already experienced also at the international level and playing at the highest level. Kevin Mbabu is also playing in Bundesliga for Wolfsburg. 11 games for the national team but definitely a familiar name for the FIFA players!
Fabian Schär is another experienced defender and plays in Newcastle. 54 games and 8 goals which show how big of a threat he is in the box.

Midfielders - It feels like Xhaka and Shaqiri has been there for ages. 28 and 29 years old midfield pair playing in Arsenal and Liverpool at the moment. Both have been playing on a high level for years. One problem, though, Shaqiri is more like a fringe player in Liverpool at the moment. 180 games with 35 goals combined between them for the national team.
Steven Zuber and Denis Zakaria can be counted as 'old faces' also. 66 games and 10 goals combined. Rather holding and defensive players compared with Xhaka and Sahqiri.
Both playing in Bundesliga as main players, so getting good experience in strong leagues. Then there's Remo Freuler. 27 games with 3 goals and playing for Atalanta. One of my favourite teams to watch. Speedy and attacking team. They are the core of the midfield, for sure.

Attackers - For the goals, they are looking to Haris Seferoviv, Admir Mehmedi and Breel Embolo. The first two are in their thirties and combined 145 games with 31 goals. Seferovic plays for Benfica now but has played in Bundesliga and Spanish La Liga as an integral part of the team. Mehmedi has been playign in Bundesliga for several seasons.
Breel Embolo should be the future of the Switzerland attack. 24 years old and already 42 games for the national team. Had an amazing season with Borussia Monchengladbach last season but more goal-shy this season. 

Overall expectation

Switzerland is priced around 1.6 to qualify from the European Championship Group A and to be in a close fight with Turkey and Wales based on odds and my opinion. 
A good mixture of seasoned veterans in their prime years and some youthful energy. They need Embolo to start banging in the goals, and maybe Shaqiri can use his energy he has been saving in Liverpool during bench warming. 

I hope to see them in the playoffs and put them in 2nd place in the group ahead of Turkey and Wales. They will go against the 2nd placed team in Group B in that scenario. Russia, Finland or Denmark will be the opponents if Belgium will win the group as expected and these teams should be below Switzerland.

European Championship Group A - Wales

Outsider in the European Championship Group A. But, this may do a favour to them. Odds around 1.8 to make the way of the group, so it will be a close call.
Squad value around 112m, and if we remove Gareth Bale from the equation, the team lacks a star, goals and experience on the high level.

Wales sits in 17th place in the FIFA ranking. No 'big' results in their recent games. Beat Czech, Ireland, Finland and Mexico in recent games. Lost against Belgium and England as expected. 
Manu legend Ryan Giggs is the head coach of the team, and he hopes to reply to the success they had in the 2016 Euros. Despite being the underdogs on every step, Wales reached the semi-finals! They beat Belgium in the quarte-finals and were kicked out by Portugal.

Potential squad

As expected, the squad consist of players mainly from Premier League, Wales local league and English lower leagues.
There are some solid teams where the players are listed. I said listed because the issue is that the players are not main team players there.

Spurs, Liverpool, Manu and Juventus are schooling seven players in the squad list. None of them are the main team players stepping the field week in week out.
The future looks good tough, as most of them are young players fighting for their place.

Goalkeepers - Wayne Hennessy was the main goalkeeper for several seasons in England Premier League for Crystal Palace and will also be the main man for Wales. Danny Ward and Adam Davies are also in the Premier League, but rather back up goalkeepers.

Defenders - Two players are playing for the Spurs. Ben Davies, if healthy, will be integral in this defence. 28 years old and 58 games for Wales.
Joe Rodon has got some games this season for the Spurs but has only 12 games for Wales.
Chris Gunter can be called a seasoned veteran with his 100 games, plays for Charlton. Chris Mepham, Connor Roberts, Rhys Norrington - Davies and Neco Williams are also playing in Premier League. Neco has got some games for Liverpool and a lot of praise from Klopp. A young but with a great potential core in the defence, looking for the future.

Midfielders - Veterans Joe Allen and Aaron Ramsey have more international caps than the rest of the midfield. Both are still active players, but Ramsey can't even get into the squad list for Juventus for most games. Joe Allen plays in the Championship, but at least he plays!
Jonny Williams and Harry Wilson are playing for Cardiff in the Championship also. Wilson had a decent season for Bournemouth last year with 7 goals. 
Ethan Ampadu and Daniel James have to carry this team while being 23 and 20 years old but have shown some strong performances in the Premier League for Manu and Sheffield.

Attackers - Gareth Bale. 90 games and 33 goals. A not too long time ago known as one of the most lethal wingers in the game. Can he make a comeback in this tournament? A hat trick against Sheffield United may mean some good things. 9 goals in 16 games for Spurs points to correct direction also. 2 goals in 16 games in Real Madrid may be behind him; only time will tell. The fact is that Wales needs him and his goals big time.
A potential alternative is Kieffer Moore, a strong season for Cardiff City in Championship with 20 goals in 41 games. 5 goals in 15 games for Wales is encouraging also. Can he do it against Turkey and Switzerland? Time to prove.

Overall expectation

As I said before, and also according to bookies odds, they are the underdogs in this group. Not too big underdogs tough, and Turkey and Switzerland can be beatable on a good day.
They need one good performance or a lucky goal and can make it out from the group stage. Anything further would be a big success against the odds.
They lack a list of big names like Turkey and Switzerland but can outplay them with their future prodigies if everything clicks. Just hope that Giggs can make them play their hearts out in European Championship Group A as they have done before in the big tournament.