What wire?

People argue over what size wire you should buy for any application you can think of. Companies want to sell you over-spec'd high-margin products. I believe in buying as much as you need and no more.Both your speaker wire and amp power wire should basically let the current flow and restrict it minimally. Too much current restriction and the wire heats up and can cause component failures (amp) or attenuate the sound (speakers).

Speakers:
This link has a wonderful, lengthy discussion about speaker wire. My take away is that 16 gauge should be fine. I think that 18 would be OK also. I might do 18 to make it easier to run through existing channels. 

Amp:
The manual for the Alpine amp says to use 8 AWG (gauge) power wire, so there you go. I was looking for an Input Current spec as a check, but that seems to be unavailable. 8 AWG sounds like the right thing to do.