I had a lot of fun playing Sauerbraten (Cube 2). Its gratis and open source together with the server.
The graphics are good, the controls fluent. I never installed the server part but the client part was very intuitive so I suspect the server to be as well.
I played the game ~2005 on a regular (i.E. not gaming optimized) computer so it can most likely run on your hardware as well.
The game is a classical First Person Shooter for multiplayer. It has a Single Player Mode, but I always felt it more like a tutorial.
Some screenshots from their website: