Hi Jamie, depends on your age, budget and experience. Age because you're going to have to insure it. Budget speaks for itself, and experience because if you're good with bikes you can go for a non-runner and take it down yourself, otherwise look at a running bike and take it from there.
Check out E-bay for project bikes, talk to friends, amazing how many people say "Oh, you're looking for a bike? I know a mate who's got a xyz sitting in his garage"
Probably an older 250 jap would be a good place to start, cheap to buy, plentiful parts and not too difficult to play with. Or you can go old British tin, I saw an amazing BSA Bantam 175 a few months ago which the guy reckoned had cost him 350 quid total. Bike was free from a friend's Dad and the rest he made himself or got off E-bay and local breakers.