I am not up-to-date in the cpu war; however, the Intel Core 2 Duo were previously killing the AMD's (I am not sure if this has changed). I do not think you can go wrong with the Intel C2D.
The three biggest things you need are:
1. RAM: Atleast 2GB (the more the better)
2. CPU/FSB/cache: Intel Core 2 Duo. Obviously the faster the clock speed the better. 800FSB is very nice. 4MB cache is ideal but not necessary.
3. Hard Drive: Try to get a 7200RPM vs a 5400RPM. This is critical and maybe the most important even though I've listed it 3.
Here is what I was able to quickly configure to meet your needs for $1278 from Dell. I don't have much experience recently with HP but a few years ago they were awful.
Dell Inspiron 1720