There's your problem lmao. That and your processor. If you want a good cheap graphics card I recommend the Nvidia gt 730.
Well, with those specs his motherboard might need to be upgraded too. Might as well start fresh while maybe keeping the case, PSU, some cables, and some peripherals. Though with those specs I bet the monitor needs an upgrade too.
But anywho, any games that can be run on DOSBox, any classic console or handheld emulators, and any game from the early 2000's should run on your PC.