Best games to play with your girlfriend ever. In my case wife. She's played super mario a couple times as a kid, that's about it. Close enough.
Alien Isolation OR You Don't know Jack OR Pocket Card Jockey OR The Cave OR just about any adventure game with some humor OR load up an emulator and prey on her nostalgia
I strongly recommend any old point-and-click adventure game. Any of the old LucasArts adventure games are great. I highly recommend starting there.
Those types appeal to all sorts of people. Otherwise, maybe an RPG, because with either of these genre you can make decisions together, solve puzzles together, and you'll most likely travel with a party, so you will most likely both have a sense of agency. I would not delve into more complex games until you get her feet wet and find out she likes it, so classics (16-bit era and earlier) are your best bets.
As far as playing games go, have you tried playing Doctor with her?
Hammer Watch BattleBlock Theater Crawl Castle Crashers Realm of the Mad God LEGO games,the older the game, lower spec they run on. I had Lego Batman running on a pentium 4. Trine? Torchlight Doctor BroForce Crypt of the NecroDancer Full Mojo Rampage Legend of Dungeon Hide the sausage The Binding of Isaac: Rebirth Dead Pixels Shovel Knight: Treasure Trove Fight The Dragon Shadowgrounds Darkstone