isn't necessarily going to be the answer. Some routers are very much better than others, and depending on the layout of your computers a cheap model might be a total waste of money.
My personal preference is for a Netgear wireless router which has a built in cable/DSL modem. This will cost you £104 (inclusive of VAT) from click here It comes with a 128bit WEP encryption algorithm, so no worries about "pesky neighbours" - not that your wireless signal is likely to reach that far anyway.
All you need then (as you correctly said) is a wireless network adapter for each machine. This doesn't have to take the form of an internal card, there are some very neat little USB models available which makes installation a breeze.