See
ntl's minimum computer specifications - yes, that'll do. Incidentally, if you don't have an ethernet port, you can get an ethernet card for less than a tenner, and it's a much better way of connecting than USB.
Also, if you want to connect your other PC as well, you can get a router, which you put in place of your PC as it connects to the modem; you can then connect up to 4 PCs (for a normal wired router) to that - they can all be connected to the internet - and to each other - at once. Most routers will include a 'hardware' NAT firewall, which is some of the best security you can get. Routers come from about £40+ (there are cheaper, I think) and are usually a doddle to set up.