I suggest the Athlon 64 over the Pentium 4 for a few reasons:
One, you may have a useable upgrade path if you go with the 3000+. AMD has said they will continue making socket 754 processors as long as their customer's demand such a thing. However, socket 478 processors are going to stop at 3.4GHz.
Two, the Athlon 3000+ will perform better than the 3.2GHz P4 in many games and general usage applications. Also, you should be able to overclock by 100-200MHz. Since the Athlon 64 scales very well with clockspeed, you should see some significant gains from an overclock of that level. It is always good to go with whichever CPU is clocked higher by default, if their estimated OC performance is similar. Why? Because overclocking is luck of the draw; the difference between a P4 system that overclocks poorly and an Athlon 64 system that overclocks well will be less than the difference between a P4 system that overclocks well and an Athlon 64 system that overclocks poorly.
Three, if you plan on keeping this system for a decent length of time, then 64-bit software support may become more prevalent. This will definitely give the Athlon 64 a nice boost in performance. As well, because of the infancy of Athlon 64 based system, performance should improve in other areas. Improved chipset drivers, motherboard BIOSes, and other software support should all help the performance of the Athlon 64 platform over time. The Pentium 4 is pretty mature, so I expect performance increases to be less noticeable.
Four, if you go with the P4 system, you will either have to buy 2x256MB sticks of memory, or you will have to go with a single channel setup. So, you either have to reduce the upgradability of your system, or you have to have temporarily reduced performance.
Here is the build I have put together:
Case: Antec SLK3700AMB ($60)
Mobo: Gigabyte GA-K8VT800 ($100)
CPU: AMD Athlon 64 3000+ Retail ($227)
Memory: Buffalo PC3700 512MB Winbond Module ($102)
Total (Shipped to MD): $504
Beyond the system setups you and the other posters have mentioned, you should also consider an Athlon XP system. You could get a 2500+ and attempt to overclock it to 3200+ levels. A lot of people have had success going this route. You could save a lot of money on the CPU and motherboard. You could take that money and put it towards a faster video card. That Radeon 8500 is going to limit the performance of your system. I know, you probably plan on getting a better video card later, but I just thought I would throw in this suggestion for whatever it is worth.