I am a fan of SUVs for towing, because of the secure storage with convenient access. I towed happily with a Toyota Sequoia for 3 years.
So far as gas mileage, you are not going to get significantly more than 12 mpg even with a streamlined trailer. And that will vary a lot. You can save some gas by driving slower and less. Your tow vehicle will also be your daily driver, so gas mileage can help you out there. I am a Toyota fan, BUT the Ford Ecoboost engines are getting a good rep for both towing and daily driving.
If you don't want/can't find a SUV, next best thing is a truck with a hardside bed topper, the taller the better. An extended cab will give you some more storage too.
You need to carefully match your RV to the tow vehicle. The limiting factor is likely to be the cargo capacity of the tow vehicle.... not the amount that's listed as the towing capacity. So carefully calculate what that is, and what you will need to add to the empty weight. Your cargo will include the tongue weight of the trailer (10-15% of the LOADED trailer weight), the hitch, all your gear in the truck, and the 2 of you.
In your shoes I would go to some RV shows, or at least to some dealers where you can actually LOOK AT and GO IN some of the RVs you are considering. Think about what you like to do, the way you use your spaces, and visualize yourselves doing that. Do you need desk space to work? (Many people buy a bunkhouse RV and convert that space.) Can you deal with a bed where one of you has to climb over the other? Do you need a place to sit besides the bed & dinette?
If you want to be frugal, you will likely stay in some park/forest service campgrounds with no hookups. For that you will need good-size holding tanks, a good battery bank, and some sort of generator and/or solar charging setup.
So decide on the type/style trailer you want, get an idea for the weights, and then start looking at tow vehicles. Decide the general type you want, figure out if it will work with the type trailer you want, and then start shopping for both.
Single empty-nester in Middle TN, sometimes with a friend or grandchild on board