You can probably cover about 2/3 of the games in the market with one hand. Just about anything that runs turn-based should be fun, even without a hardware upgrade. This covers everything from a large swathe of the 4x strategy games, to most Rogue-like games to puzzlers.
If you add a new multi-button mouse or other OTS capability enhancers, racing games (limited control set) and single player RPGs (those that pause when you bring up inventory or other data screens) come into play. RTS may also work, but could cause trouble if some of the game actions aren't accessible from mouse menus.
For an RPG, you'd need that tab button, plus buttons for forward and backward movement, and a button to pick up things, when you add in the 2 standard buttons and the wheel, you're probably looking at an 8-button mouse as a minimum (you'll turn your facing to move sideways, unless you add more buttons). Some RPGs that require you to use keystrokes to enable special attacks could be problematic. You won't be taking on the really combat-oriented RPGs here.
MMOs and FPS are probably the last thing you'll be able to take on and feel competitive - they'll probably require a prosthetic or some alternate control mechanism to provide a full substitution for the "lost" hand. And whether you elect to go with additional hardware or not, the learning curve will hurt your gameplay for a while.
Finally, if your other arm has any useful movement that can be restored with PT, there's a good chance it can still be used for mashing the spacebar or a virtual equivalent. And best of luck to you dealing with this IRL as well as from a gaming perspective.