Graphics card is getting on a bit too. As mixture mentioned i5 minimum (preferably i7) but the graphics card is where the work is done for games so a GTX780 or later will be better.
Obviously all this will put the price up but I reckon you will need to spend around £1000 for a box if you don't want it to start wheezing on the latest games too quickly. Keyboard, monitor etc will be on top of that.
I had a good experience with Dino PC on my current computer.