Nice looking router
And yes, it will work, perfectly. It is made for Cable/DSL technology.
The wire between the modem and router, should indeed be standard ethernet if i recall correctly.
Virgin Media will actually provide you with this cable, as it comes with the modem.
Everything else you mentioned is perfect. Tot's advice above is spot on
Don't be afraid to ask the installer about routers though, they may well, out of the goodness of their hearts install it for you anyway if you ask. Just be prepared for them to say no, as they're technically not meant to
