100 AMP garage sub-panel from 200 AMP house
Your options are a minimum of #1 aluminum or #3 copper.

Since it's only 65 feet I wouldn't upsize it for voltage drop.

You don't need service entrance or direct burial type cable if you are running conduit underground you can use type THWN wire. Individual wires not cable. If you don't want to run conduit you can buy direct burial type wire like You are talking about.

Good luck and stay safe!