The most important thing for photo editing is to get a good monitor, one that has a wide-gamut and can be color-calibrated. Those vary in price but can be gotten for as low as $450 USD for a new NEC Multisync P221W. Can spend more and get a similar model up to 30" in size but that depends on your budget.

NEC sells them with or without calibrator. What I did is buy the 30" model with and two P221W without (Refurbished for $237 each!), since the solution is the same and the difference is relatively smaller on bigger displays.

Now I am not sure if you intend to buy a pre-built computer or build one yourself. Regardless, make sure you get one with a lot of memory, 4GB or more and make sure it is a 64-bit computer with a 64-bit version of Windows 7. Nowadays, almost all computers other than small laptops are 64-bits but they do not always install the 64-bit OS which gives application limited access to memory.

You need to get a computer with a graphics card. Which one? Pretty much any will do but you have to have one. Cheap computers come with embedded graphics which is not as good.

Those are the basics but read more considerations here. The exact parts have probably changed since the article is 1 year old but all the recommendations are still good.