Good luck leaving AOL, I hear they can be quite difficult to shake off. You'll get a lot of different answers here with everyone recommending their own ISP - it depends what you want in terms of speed and download limits as to what's best
If you have Sky TV, look at their broadband, I'm on it now and can't recommend it enough. �10 a month for upto 16MB and no download limit - I usually get over 10MB
BT's broadband is overpriced and their customer service is shocking. I left them to go to Sky. Orange, Tiscali and Talk Talk are generally regarded as being pretty bad as well. I've read mixed reviews about Virgin, apparently their cable based service is pretty good, but their ADSL service - normal phone line, is not so good.
Do a search in Google for broadband reviews and see what you get