Personally, I've tried a lot of them, and so far:
Finspreads are good for starting off, particularly for 1p trades for 8 weeks then minimum 50p trades. Their platform can be significantly slow, especially at peak trading times, though.
Worldspreads (same people as Two Way Spreads, right?) are cheap, fast, but don't offer a lot for the starting out trader.
CMC Markets have a pretty platform, but can be a bit of a shambles; requotes are common, and a lot of people complain about their datafeed "spiking" to hit stop losses.
IG Index, who I currently use, are the best all rounder so far. Like FinSpreads they do an introductory course weeks, and they do low minimum trades (10p, then 20p, then 50p, for two weeks at a time).
The reviews section of this site might help. Don't be afraid to open a few accounts and see who you like. Oh, and if you do want an account with IG, I'd appreciate getting referral credit, if you don't mind IMing me a name and e-mail address?