what sort of APIs would be most useful? Player/matches stats, other stuff?
Basic API endpoints for players, weapons, factions, characters, and leaderboards would be a great starting point - useful for building out fun dashboards, profiles, dynamic images, etc. Endpoints for matches, maps, gamemodes, etc. getting into the real gameplay data would be useful for more challenging neckbeardy stuff. I noted a few example endpoints and use cases below.
Any example of game APIs u like?
I don't have any examples for games APIs that I play
&& use, but Riot Games' API and Battle.net Community APIs (WoW, Starcraft, Diablo) look great and are well-documented. If it doesn't have great documentation, it's not a great API IMHO.