It would be a very bad move to stick to Intel unless you're going with a C2D and since you want to keep your memory an X2 3800+ i think would be perfect for you, it'll definitely be faster then your P4 even if the clock speed is lower...don't be fooled by clock speeds, architecture of the cpu as a lot more to do nowadays, hell even my athlon xp rigs are faster then higher clocked P4.
I think that stevemc's suggestion would be perfect for you if you plan to overclock in the future.
But for a budget build for gaming and school work here's my sugg :
Athlon64 X2 3800+
( i can't seem to find any though, maybe they stopped the production ) Back Order at tankguys.com (165$)
Asus A8N-E (74.99$)
Video card :
e-VGA 7600GT(130$, 110$ after MIR) Best bang for the bucks in the mid-range area.
Antec TruePower II 430Watt (70$)
Or any Antec powersupply that seems right for you, they're cheap and made of good quality. Just don't get a no-name one.
Hard Disk :
Western Digital Caviar SE16 250gig (80$)
Depending on what you have at the moment, it's not nice to have a powerfull computer and being limited by the hard drive, the SE16 are real nice drives and are more then affordable.
For a total of 440$ or 540$ if you get the extra drive.