The bad news is those specs won't run much of anything... the good news is, most of the things in the under $5 section of the store actually /are/ old enough to run comfortably.
Some recommendations by genre:
Roguelike: Dungeons of Dredmor
Strategy: Sid Meier's Civilization III Complete
RPG: Haven't played this personally (I own it, but haven't had the time to try it) but the Cthulu Saves the World/Breath of Death VII double pack is only $2.99
Platformer: VVVVVV -- one of my personal favorite games of all time, incidentally
FPS: Jedi Knight and Dark Forces are both $4.99, although be warned that they're old -- Jedi Knight is a Windows game from the mid 90's with all the little annoyances running it on a modern system entails (not to mention a redbook audio soundtrack that you can't get in the Steam version without a fairly complicated workaround), and Dark Forces, while awesome, is a DOS game that came out around the same time as Duke Nukem 3D.