South Dakota, Texas, and Florida are best these days. Everyone in on the lookout for montana LLC's, don't even go there.
What you are really looking for as a full timer is a "domicile state". someplace to call home, when your home is on wheels.
You'll need / want to register to vote in your domicile state, get your drivers licenses there, and your license plates.
This is also where you will pay state taxes 8if they have any) and where your home as far as medicare or other health insurance is.