Priority (1) - Uni work (Programming, Circuit Design, Word Processing, Excel etc..). In other words, it should be able to perform multiple "mundane" tasks at the same time without too much trouble. This includes web-browsing with a ton of tabs.
Priority (2) - Gaming. Games like GTA IV, GTA: SA (with mods), Guild Wars etc .. and I want to be able to run them at mid to low detail at around 60FPS.