Yuck, dont get the Athlon XP, that AMD64 3000 is dirt cheap. I dont know how old your are, so if your younger money is hard to get. School/job takes alot of work. Just stay with that 3000, just to remind you, the 3000 really run at 1.8ghz.
Like i said, i dont know your money issues, but i dont recommend the 3000 personally. If you can manage to get a 3200 socket 939, it would be alot better. The 3200 runs at 2.0ghz, i wouldent get any AMD64 that runs under 2.0ghz.
For that question you had, "Why are 64bit processors better then 32bit processors". Heres a simple way of understanding it. Would you rather have a 128bit video card or a 256bit video card..? In a few years 512bit video cards will be released, then a few years after that 1024bit video cards will come out. Processors work the same way. 64Bit is the near future of processors.
But, nothing is compatible with 64bit processors yet. But they also work as 32bit processors, witch enables them to work with present software.