There will be detailed settings in the amps menu to set which video output goes with which sound output. Most will be quite flexible in this regard.
Yes a Wii can be connected up, I have mine connected via component for picture and then left and right phono for sound. if you a re investing in a home cinema a separate amp and speakers is certainly the way to go, far more flexibility and future proofing.
You don't have to break the bank nowdays either as as Sony, Denon, Yamaha and Onkyo all offer decent entry level units, this is a selection of the most popular
http://www.richersounds.com/products...s/av-receivers
you certainly want to make sure you have HDMI switching and HD audio, most in the £200-£300 bracket should offer that. I replaced my 10 year old amp a fem months ago with the Denon 1910 which is a beast.