I guess you don't really know what kind of games you like?
Some good ones to try would be Skyrim or The Witcher 3 or Fallout 3, New Vegas, and 4 for open world RPGs, Road Rampage or any Need For Speed game for arcade racing, Mini Metro for a casual puzzle game, Stardew Valley for a casual farming/life sim, Bioshock 1, 2, and 3 for a first person shooter, the recent Tomb Raider games for third person adventure, Dishonored 1 and 2 for stealth, Civilisation V (or any other) for turn based strategy.
Well, really just go find super popular games and give then a go. Easiest is to get them on Steam and they should just work on Linux and refund them if they don't, though you can still play non-Steam games and you can check on protondb.com if others have had success (Proton is Steam's wine-based tool for playing Windows games on Linux).