I’d go down the route of so called ‘Walking Simulators’* though I use the term First Person Experiances, such as Dear Esther, Gone Home or maybe even Firewatch. Games were you can take you time and practice the feeling of movement. From there if you are looking to get into shooter style games go for something Co-Op. My wife and I started on Time-Splitters where she basically stayed back as a sniper whilst I ran in. (This was back in 98/99) From there we ended up going through Halo, Gears and eventually Borderlands as they came out. Anything where you have a bleed out / respawn mechanic is great.

*For me a walking simulator would be more like Octodad where you actually have to work at the walking! :D

Probably not quite what you meant but two monitors for Dwarf Fortress is a god send. Game on one screen, the other for DFHack console, Announcements, SoundSense, Dward Therapist, and various other utils. Could probably use 3 actually…