Most full timers pick a state friendly to full timers and use a mail forwarding service in that state.
There are several things that make a state friendly - let you use your mail service street address on your drivers license, remove you from the jury duty rolls, make it easy to register to vote and to become a resident, no state income tax or tax on dividends or interest income.
The three most popular states are SD, TX, and FL.
We picked SD and use
Alternative Resources for our mail forwarding. They can also provide help and services for your change in residency.
They have some good info on their site in the link above.