DPP runs mutli-threaded (at least it does running on linux via Wine), so in that respect the more cores the better. I get away with 4gb of ram easily (although straight after boot i'm only using 300mb of ram, 8gb would be nice for winbloats).
So in that respect, my Phenom x6 2.8GHz and 4GB ram does the job nicely. (go for 8gb minimum if getting win)

But when I stitch, or HDR, maybe it's the programs I use (Hugin, Luminance), they run single-threaded and chew huge amounts of ram. Like up to 16gb of virtual ram (swap) space on my SSD and then some. stitching and tonemapping takes heaps of time (5 minutes for a standard 18MP tonemap) because it's only using a single core. I'm going to chuck in an extra 8gb or 16gb ram some day to help with these shots, if you do them regularly or want to try, go for a minimum 16gb off the bat.
Generally, whatever programs you're using, best check if it can run double/multi-threaded, if it can, get as many cores as you can. Multi-core AMD Phenoms are dirt cheap, as are their motherboards. Multi-core Intels I haven't kept up with the market lately, but normally they're less performance/$ (especially counting a good motherboard) than AMD, they just have a lot better performance in absolute terms.