Let's kick off the ones that already had games that were fun and worked.
Punisher. He's had a few including the PS2/Xbox one that was gritty as ****. His games should be a no-brainer as long as you don't mind getting down and dirty.
Spider-man has his formula down pretty good by this point.
Hulk. We need more games for him like Ultimate Destruction. That game was the **** and I had a blast with it. Surfing on buses, car boxing gloves and the rest was amazing.
When I think of an Avengers game I can't help but think of the old Arcade style ones with the Albino Vision. Side scrolling beat-em ups like the X-Men one with Dazzler. The other way is Ultimate Alliance. I don't see it working any other way unless they surprise me.
As for the other characters -
I can see Hawkeye/Black Widow working in a Metal Gear style game. They both kick ass in a multitude of ways, have a large variety of skills and lend themselves to both long range and close fights.
I really can't see a Thor or a Captain America game working that well. The first is too powerful to fight anything except other gods/giants in Asgard. The second is basically Batman without the toys and would be seen as one due to all the Arkham games.
Black Panther could work as a global conspiracy game. He finds out about things dealing with Vibranium, it being stolen or whatever and he is out there dealing with both the politics and ass kicking parts of the story. It would be similar to Mass Effect for the politics with both the speech wheel and choices that follow you. You could play as a kind and generous king or a jerkass that wants his **** back and isn't above intimidating people.
I'm still irritated over the FF Silver Surfer game so I'm not going there.
X-Men would be fun since I love the team games. Legends/UA are great fun and even the Marvel/X-Men vs whoever ones are great as well. Destiny was mediocre but I'm sure most of us know the story behind that.
Seeing a bad guy game would be fun. Run things from Dr Dooms POV or the Green Goblin would be fun.