Steam has Proton now which is a god send for Linux gaming. https://www.protondb.com/ which is just a setting in the Steam client.

For games it depends on what might interest you. If you are into history sorta stuff, maybe Civilization V or VI? If you want more of a fun game that a lot of non gamers play, you try The Sims or Stardew Valley. If you want something like the current trend of games, try Helldiver’s 2 or Baldurs Gate 3.

If you ultimately don’t have a preference. Just browse the sales on steam for games that look interesting as well as browsing https://www.humblebundle.com/ which can sometimes be good. Just check it against that protondb or look up if the game runs good on Linux first before purchasing.