You have a considerable good budget for a gaming computer.
A good sugestion is a quad-core processor, you can choose between Phenom X4 or Core 2 Quad.
If you wish to really spend with processors, Core I7 or, Phenom II X4
Examples:
Core 2 Q6600
Phenon X4 9950
Or, if you feel like, a good dual core processor, such as: Core 2 Duo E8500
Good motherboards marks is like: Asus, ECS, Gigabyte, MSI.
Asus seems to lead in market, with awesome motherboards.
A good example is: Asus Rampage series.
But, Asus works better with Intel.
for AMD processors, ECS Motherboards are recomended.
Video cards, choosing one is not very hard.
If you wish to have a good gaming experience with Nvidia, GTS250 or 9800GTX+ seems good enough.
with ATI, i could say: HD 4850 or HD 4870
Power supply:
Choose between: Corsair, Huntkey, Seventeam, Coolermaster, C3 Tech (750W Model Psh-750v Only), OCZ.
Well, you're going to need above 500W.
Do not choose cheap or generic marks, such as Clone, Choose only above.
Memory:
800 mhz is a good choice.
corsair, kingston, markvision, ballistix and OCZ are the best marks that i ever experienced :P
If you wish more peformance, 1066 mhz is a good pick.
Casemod:
Choose a big case, for cooling reasons.
Gamer casemods is a good choice.
Monitor:
LCD..
I'd choose 15,6" or 17"..
i personally don't like LCD monitors with like 30"