It doesn't matter in the end: just go with the ISP that offers you the best deals and service.
If you already have a modem, then check how it connects to your computer. If it connects via USB, then you'll need to buy a modem+router in one. If it connects via ethernet (RJ45), then you can just get a router. Finally, if you need a modem+router, then make sure it's either an ADSL modem or cable modem, depending who your ISP is (cable means telewest or NTL basically; ISPs using your regular phone line are ADSL).