A large safety pin stuck in your paper towel roll will keep it from unrolling while you're moving. It can also be used to poke a hole in eggs before you boil them to prevent cracking. Stainless diaper pins work great.
Be certain that your spare tire is the same size as the rest of your tires and that the rim is the same and will fit the bolt pattern. Do this by removing the spare and putting it on a wheel! You will also find out if your spare tire is easily removable.
Take the wheel locks (lug nuts with a matching "key") off your wheels; they can get stripped and the key can get lost under off-highway tire-changing conditions.
There is no tire that will stand up to off-road abuse as well as the B.F. Goodrich. It is the only tire with a three-ply sidewall.