I build this machine for a family member who plays WoW, its a low-mid budget machine which will run every game thrown at it (high spec games on med settings) and runs WoW perfect at high settings.
Intel Core i3 2120 3.3GHz
Corsair 4GB (2x2GB) DDR3 1333MHz
Casecom MA-1199 Shiny Silver with Black Front MATX Tower Case
TP-Link Wireless-N150 PCIe card
Total cost aprox £200
GPU a GTX 560 ti is plenty for wow and cost around £150
If that means 'hang out in old zones questing and picking flowers', then go with something like zink's build. Super cheap. Pretty much anything with discrete graphics (and some newer AMD APUs) will play WoW by that standard.
If it means 'casual battlegrounds, arenas, dungeons, maybe the occasional 10m raid, lots of instances and zoning' then go with Screwy's - you'll enjoy the SSD.
If you want to do LFR, 25m raids, serious 10m raiding, or if you want remotely playable framerates on world bosses and boss rooms in AV/IoC, though, you need to get more serious about the CPU. The one I'm suggesting is overkill, but it can't be beat in terms of bang-for-buck, and downgrading it doesn't really let you upgrade anything else in a major way until you cut at least £60 off the price. (I guess £30 cheaper would get you a Radeon 7870, so you could maybe do a core i5 2320 with a cheap 7870).
This is my suggestion if your WoW-playing involves a lot of large-scale combat at max level: