Pretty much any new computer will quite happily run premiere pro, even the bargain basement entry-level Dell PCs will, but not very well. Go P4, not celeron.
I'd look for at least 512MB RAM, at least 160GB Hard Drive space (although there's no such thing as too much hard drive space, get as much as you can afford) and, as video editing doesn't (as a rule) stress the video card much, a cheap entry-level geforce or radeon card should do the trick.
A lot of people will normally recommend an AMD64 system (me included) but if you're set no buying a Dell, then they only supply intel based systems. At the moment