<<< I am confused between the speed offer by my broadband provider IDNET (somewhere between 2-5mbps) and the speed of the router. >>>
If you subscribe to a 5Mbps service with an ISP, you have a connection that will allow you to download at speeds of up to 5Mbps. Your home network, the connections between PC and router and between different PCs will run at 100Mbps for wired ethernet connections and 54Mbps for wireless connections using 802.11g protocol.
<<< If I use the router to connect to the internet will one of the computers have to be on to allow both to connect to the internet? Is there any way around this? >>>
When you install a router, it is the router and not one of the PCs which establishes the connection to the ISP. All computers connected to the router get their internet access over the LAN from the router and no computer is dependent on any other computer for internet access. They are totally independent.
<<< Can I just plug an external drive into the router to allow me to back up data or does it need to be connected to a pc? >>>
There are external hard drives with an ethernet interface, but these are more expensive than the more usual USB 2.0 or Firewire drives that need to connect directly to an individual PC.
<<< Any suggestions as to which router - I am happy to spend c£100. >>>
With ADSL, you want a combined "Wireless Router & ADSL Modem". Models from any of the mainstream manufacturers should be fine - Belkin, Linksys, Netgear, D-Link. One of the more popular models is the Netgear DG834G