What type of wire should I install

copper

High speed HDMI + Cat 5e + speaker wire. Lighting control might require some additional conductors as well.

And add conduit (smurf tube) if in doubt

You need to decide on a distribution point in the house. Run Cat5e (or Cat6) and 4 conductor speaker wire to a volume control/keypad location in each room. Then run (2) 2 conductor speaker wire from the volume control/keypad to the speaker locations in that room.

This will give you the ability to have a basic volume control system right up to a full blown Crestron system. Unless you want touchscreens in each room, then I suggest calling a local AV company.

I don't know why someone suggested running HDMI?

Run at least stereo speaker wire to each room, looped through volume control/keypad location. Run cat5e/6 to volume control/keypad location.

You might want to run surround sound speaker wire (so six speaker cables or more) to some rooms from central location (I did that for my living room).

Run at least two cat5e/cat6 cables to each room, can be used for ethernet, hdmi, IR, audio, whtever.

Run at least four cat5e/cat6 cables to each TV location. Maybe coax too (I didn't but I live in an apartment and won't get satellite or such).

You'll never regret running "too many" cables. Too few though...

+1 !!

Decide what you need, then run 2 or 3 more CAT5e/6's to be sure! Its so cheap to scrimp on, that you will likely regret it later if you don't!!