A budget and more specific summary of what you want to actually do on a day-to-day basis may be useful.
1) Unless your post-processing is very time critical, any recent quad core CPU should do the trick. If you are building new, a core-i5 2500(k) based system is probably quite sufficient.
2)You are going to want as fast a data storage system as possible as this will likely be the bottle neck, especially if you deal with a lot of large raw files. The two obvious solutions here are to get an SSD hard drive (such as the Crucial M4). Alternatively, or in addition, given the low price of memory, you could go the route of getting extra ram (ie, 32GB) and setting up a small ram disk for which to dump and process your photos from. You could likely get away with 16GB of ram to do this (ie, 8-12GB system memory and 4-8GB ram disk), it really depends on how many photos you normally process at a time.
3)Photo processing software has supported GPU acceleration for the past couple of years now (ie, Photoshop). So perhaps a mid-range discrete graphics card might also be beneficial (something in the $150 range perhaps).
4) The two most popular photo processing programs for the PC are probably Photoshop and Lightroom (both Adobe products). Lightroom is significantly less expensive, but offers a few limitations. My impression is that Lightroom is sufficient for 99% of a photographers processing needs. You can get a comparison of both software programs here
5)If you don't have a decent, color-accurate monitor it can make post-processing difficult.
In summary, I would start with something link TR's Sweet Spot
build and perhaps increasing the ram to 16 or 32 GB as budget dictates and maybe getting yourself an SSD (doesn't have to be a large expensive one as you can archive your photos on mechanical disks or DVDs, etc). You could also get away with getting a cheaper video card if you won't be doing any gaming. As mentioned, many filters in processing software are now GPU accelerated, but it really depends on how much post processing you do and, specifically, how often you use these filters.