Firstly, you are unlikely to make any significant saving by buying a "wired" router instead of a "wireless" one, even if you can find such a thing. The only difference is that a "wireless" router incorporates a Wireless Access Point, in addition to the conventional 4-port switch.
Secondly, there are two distinct types of Router, depending on whether you are connecting to an "ADSL" service via the phone line or Virgin's "Cable" service via either a Cable Modem or a TV Set-top box.
With ADSL you use a *combined* Router & ADSL Modem.
Have a look at models of the correct type from Netgear, Linksys, D-Link, Belkin etc.
With Cable you use a Cable/DSL Router which doesn't incorporate a Modem.