Cam - as little as possible. You can "customize" your new Casita at leisure when you are home. Primary is to spend one night near the factory and check all systems, heater, AC, water pumps, frig, etc., as well as the trailer itself. If anything is amiss, Casita is very good at quickly correcting any problems. Tougher to do once far away. Be sure to record or note the check-out procedure. Lots of information coming your way when you take delivery, especially when you are excited with your new rig.
For your way home, basic issues like you mention, TP, blankets and/or some basic bedding, basic food. Some wheel chocks if you plan to disconnect enroute. Buy a few gallons of water for use. Casita recommends you clean the fresh water tank, what's the word for it, sterilize? with some clorox before filling. You might want to have the propane tanks filled so you can check your frig on propane while on the road home. BE SURE to fill the hot water tank with water before using the electric water heater. You can turn off the electric heat with a button outside, have the staff show you.
Then travel home an begin to enjoy your new Casita. Congrats!