Generally if you’re using a standard, single-user package from most providers, you’ll need to buy no additional hardware. Virtually all broadband providers will give you a free modem, microfilter (the device which connects to the phone line) and USB cable (to connect to your computer) so you can get going straight away for no extra cost.
If you want to start sharing your broadband connection or use a wireless connection you’ll most likely have to replace the free modem with a suitable combined Router/Modem (although you can buy the router part on its own if you want – but it makes it much more complicated to set up for very little saving).
Routers generally range from £50-£100 and it’s probably worth getting one with wireless networking included it even if you don’t use it at first, as it’s not much more money and could become very useful in the future!