Third parties huh? I'll throw in my two cents. I wouldn't mind doing this for 1st party series too. But I'd keep my comments shorter.
Metal Gear: Raiden I guess.
Sonic: Tails. He's probably the most famous player 2 character since Luigi. Maybe even more so than Ken. He could offer a lot, He's able to fly, jump higher than Sonic and uses Gadgets. Yet he still could be pretty similar if he needed to be a semi-clone or echo. This makes him really flexible with the amount of work you could put into him. Wanna go crazy? Pick Tails. Want a safe choice in terms of moves? Pick Tails. Win-win situation.
Mega Man: Mega Man X or Mega Man.EXE. They are main protagonists of their own sub-series in the franchise both iconic in their own right. Mega Man X more or less setting the mechanics standard of every other 2D Mega Man game such as the Zero and ZX series(wall jumping, Dash jumping, Armors, Health upgrades ect.), much in the same way Mega Man 2 and 3 also set standards for the franchise(8-Bosses in 2. Sliding in 3, Support Items). There's also no doubt that Mega Man, Mega Man X and Zero are the most popular characters. However Mega Man.EXE is also pretty popular, and represents a rather unique era of gaming. His style of Action RPG is also unique, which could make a good basis for his moveset, whether it had gimmicks or not. I'd be happy with any blue bomber, but I feel these two are the most justified options. They have a ton of unique moves to choose from. And again, like Tails, can be justified in being extremely different despite surface level similarities.
Pac-Man: Ms. Pac-Man echo.
Street Fighter: Chun-Li. Without a doubt the most popular/iconic female fighting game character, and is probably the most popular SF character other than Ryu. Similar to Ryu, Ken and Terry, her moves write themselves. Kikoken, Spinning Bird Kick, Kikosho, Lighting Legs, and so on. And that's not assuming that she wouldn't also get a Focus attack, although she's had a few extra moves throughout the years that she may not need it.
Final Fantasy: Terra probably. Not a huge Final Fantasy fan. So I can't get into the nitty-gritty. But I know FF6 is pretty popular and I think it'd be all around cooler to get another main protagonist than any side character from FF7. And the contrast between classic FF and modern FF would be neat. But I know people would pop-off at Tig Ol' Bitties Tifa and Mr. One Winged Angel. Terra would also justify squeezing another 2 or 3 songs out of Square Enix.
Bayonetta: Jeanne, since I can't pick Rodin. She could use unlockable weapons instead, or merely be an echo of Bayo. But gameplay wise, she wouldn't be an interesting echo like Ken or Chrom.
Castlevania: Personal Bias would say Shanoa since she looks really cool. But I'll say Soma since Alucard's an AT. If he wasn't Alucard's the clear winner here. Soma and Shanoa also have a **** load of attacks to pull from.
Persona: Jack Frost. Looking out for my *****
Idon
and using a loophole to get SMT content in the game.
Dragon Quest: One of the guys from the Monster collecting ones?
Banjo-Kazooie: Mumbo? He doesn't do too much, but I guess he could implement Banjo's Transformations onto himself. Kind of like how Rosalina just steals Mario's tech from Galaxy or Zelda using Magic that we only see Link doing in-game.
Fatal Fury: Geese Howard. Cause we don't know if they'd go through with changing Mai. Micheal Jordan was right. "**** Dem kids." Also we need Kirby saying DOUBLE REPPUKEN! and SHIPPUKEN!
For those who don't like reading walls of text, I apologize.
