About 10 years ago, I sold my Lance overhead in order to transition to a TT. I spent most of the summer shopping for the trailer, so I rented a TT twice, once from a local RV repair shop and once from the Navy base close to me. The RV repair shop offered an equalizer at additional charge (don't remember how much), but the base didn't offer one. Both trailers were around 18 ft. and I had a 3500 dually so I didn't use the equalizer. The two places were quite different, the RV shop looked at the truck, had a list of things you may need, and was relatively helpful with my questions, where the Navy base person I dealt with did not seem to be as well versed in towing or camping, but they were cheaper and had brand new trailers; also they just asked if I had a hitch, proper ball and brake controller. It may be worth renting an extra day up front to just hook up and tow the trailer around to see how things operate and handle before jumping out on the road for a trip.
When I bought my first RV many years ago, I packed it, filled it with water and supplies and camped about 50 miles away just to see what I didn't know. I didn't know a lot: water heater lighting, generator operation, and worst of all, I didn't have a wine opener for my wife, etc.
When you settle on a place to rent, you may want to visit them and get an idea of what is supplied or what extras you can rent. When I sold the Lance, I stored all the stuff I took out of it in the big Rubbermaid bins, so I just loaded the bins into the rentals. Use a list off the internet or generate your own of essentials, or the rental place may have a suggested list you could use as a start.
At a minimum, check tire pressures and set to max on tires, lug nut torque, and lights before you drive away.
Good luck on your future adventures!
2011 Keystone Springdale 189
2000 Dodge 2500 4x4 V10 4.10