what games? solitare? bf2? wow? quake 3? doom 3? do you want to build it yourself or buy complete? for a generic answer and you are building it yourself i would go the a64 route unless you are going to do a lot of audio/video encoding because that is where the p4 really shines or want to buy one from dell, other than that most of your normal stuff and games(pretty much regardless of what type they are) run pretty equal or faster on a a64, considering you have the graphics card to do what needs to be done. a a64 3800+ mixed with a geforce2mx will play, if at all, quake 3 like sh!t, but a a64 3000+ with a nvidia 6800ultra would scream. also, what budget? again, this is an extremely vague answer.