As stated, full-timers who don't own a home still need an address for certain documents, including a voter's card and you can vote early by mail. We chose Texas and used the Escapees Mail Forwarding Service for 16+ years with no problems.
Since all the new medical insurance changes in the past couple years, things have changed greatly for those under Medicare age. It used to be that South Dakota and Texas were the preferred but now things have shifted if you need to purchase your own insurance. As stated above, even within a particular state, the county your address is in makes a difference.
This will really require some in-depth research on your part as to what state (& county) you want your address. Florida now seems good - so far.
There are many post on this subject in the Fulltiming section of this forum and also on other forums such as iRV2.com and Escapees.com Read the recent comments for newer information on medical insurance.
Best of luck to you and enjoy your new lifestyle. We did for 16 years!