I'm currently in a very similar situation. In St Thomas now and just back from 3 days in St Johns. We rented from Avis -prepaid - so simply picked up the car and headed to RedHook to catch the Ferry. I will say that 90% of the rentals on St John's are Jeeps - mostly the 4 door unlimited model which is what we had. The roads there are a little rough compared to St Thomas but nothing that would require a jeep. Well other that the dirt road GPS took us on to the Salt Pond. That one was pretty bad. We took the highway back and ignored the Apple Maps!
And, I wouldn't waste your time going all the way over to the salt pond. Trunk Bay, Cinamon Bay and Jumbi beache were our favorite spots. Check out the Landings for breakfast right across from the walk on ferry and the Banana Deck for dinner. Also Ronnies Pizza was fantastic for a quick lunch. We stopped at the supermarket just outside of RedHook for snacks and other food items. Much less expensive than St John's. There is also a Kmart on the way that has a fairly wide grocery section for dry goods and also has cheap beach items we don't mind leaving behind when done with them. Chairs, cooler, beach toys, etc...
Enjoy your trip and driving on the left side doesn't take long to get used to on the roads, it's the darn parking lots that give me fits.