What kind of ledge would I need? 1x4's mounted to studs?
1x4 or 2x4 for a ledger board (cleat) will work.
Yes you want them attached to at least two studs.
You do not even need to secure it to the cleats if you do not want to, It is very heavy, as long as it sized properly to not slide far enough side to side and slide off the cleat on the other end. If ...