As Batboy has said, many will supply a suitable router, some for free and some quite expensive. Or a very good refurbished one can be bought for �24 with a 3-month warranty from a site many here have bought from, not eBay!
What sort of usage do you expect to have, the good ISPs tend to fall into niches so it's horses for courses. The big ones like Talk Talk, Tiscali, Orange are as as bad as each other. I assume you know AOL belongs to Talk Talk?
Would you be happy with a 12 or 18 month contract? Not many people are these days, but a few of the ones around are fairly safe.
So heavy downloaders like the Entanet resellers such as ADSL24 and vivaciti. Entanet don't sell direct to residential customers. Another one good for heavy downloaders is O2/Be if you can get them. All of these are good.
If you have or want Sky TV then the Sky LLU packages are by far the best value, but avoid the Sky Connect package which they offer instead if their equipment at your exchange is either full or non-existent.
Top quality is IDNet but a bit pricey. Nearly as good and cheaper is Newnet - click in my sig. Zen is generally regarded as very good as well but I seem to remember a few dodgy posts about them, but very few. These are the best for speeds on "up to 8Mbps" products, plus O2/Be.
These
comparisons may help. Try your own variations on the selection I have made.
To see whether you can get Sky or O2/Be put your phone number into
here.
Hope that helps. And log in next time

. There is no need to log out really - perhaps every few weeks as the "New post" counters and things can start to screw up after a while and logging out fixes it. But that's the only reason to. Also the big advantage is that if you see a mistake after you post something, if you were logged in you can alter or delete it for up to 12 hours.