Go with virgin media if you can it is a cable service and does not rely on your BT phone line, very good service, and ive never had a drop out on it
been very impressed with it, and at the moment, its only £10 per month, bit of a bargain really for a 2Mb service, which is more than plenty for what you want to be doing with it by the sounds of things.
If you want to use it wireless then you will need to get something like this: http://www.ebuyer.com/UK/product/103185
this will work with the Cable modem that Virgin media will supply you with.
If you decide to go down the ADSL route (internet down you BT phone line) then you will need the following wireless kit: http://www.ebuyer.com/UK/product/118662
Any questions feel free to PM me and ill do my best to help.