Do you need the monitor, Windows, keyboard, mouse, etc, within that budget?
Would you really strongly prefer $800, or is $1000 equally possible?
Is overclocking important to you?
What is/are your favorite game(s)? No sense getting a quad-core CPU if your favorite games are hexa-core optimized, for example. No sense getting an AMD card if your favorite games use a lot of PhysX, as another example.
Those questions should be answered to best build a PC to fit you.