You will need a torque wrench to check the TT lug nuts on the trip home. Especially important it the TT has aluminum wheels. Most will have a sticker close to the wheel well saying how often to check them for the 1st XX amount of miles. If not ask.
Take a tire pressure gauge to check the TT tires pressures as well as the TV tires. If you have a 12v or cordless compressor take it with you. TT tires should be inflated to the max pressure on the sidewall.
Check and see if the TT comes with a lug nut wrench. The TV one may or may not work depending on size. See if they have a jack that will work with the trailer or an Anderson EZ jack.
May or may not need tow mirrors depending on how your truck is equipped and your comfort level of towing.
Some systems on the TT work on 110, 12v and or propane. Make sure they work on each system not just one of them. Fridge for example as already mentioned.
Make sure all windows work as well as vent covers and fans.