If you want a small computer to be able to put away out of sight, or just don't like seeing lots of wires, then yes get a laptop. Otherwise a desktop will be cheaper (or at least, more powerful for the same money), and as theren911 says, easier to upgrade if you need to.
If you're already on NTL then they do a pretty decent package that's �30/month for the standard TV package, 2MB internet connection, and phone line (I believe with free evening and weekend calls, if I remember correctly). You'll just need to phone them up and speak to them.
If you want to be able to use a laptop wirelessly, i.e., be able to wander around the house and surf the web on your sofa, then get a wireless router also.
Something like this.