The very first step to becoming a FullTimer is to decide which state will be your domicile, the place where you are a citizen and upon which you base all your paperwork.
Don't use the term Residency out of context; in each state, there are residency requirements for a lot of things, from hunting/fishing licenses, homestead exemptions, voting, school tuition, etc., and they may all be different even in the same state.
Be careful not to violate your claim of domicile in one state by claiming something in your old state, like a resident fishing
license. Owning property while on the road may influence this.
Why do you care about domicile? That becomes your base for a number of things, bearing in mind that you may not actually set foot in that state for years:
State Income Tax -- You want to be in a non-income tax state (I believe there are still seven of them, like Florida, Texas, South Dakota, etc.)
Driver's
license -- You want the longest period before renewal in person is needed.
Vehicle
Registration -- You want to be in a flat-fee or weight-based fee state, NOT a state that taxes on the value of vehicle (Like CA, GA, AZ, etc.)
Vehicle Insurance -- Insurance is generally based on where your vehicle is 'principally garaged'.
Emission Requirements -- State or city may require you to return to have vehicle inspected. Some, like TX, require inspection within xx days of returning to state, others may not renew without inspection.
Sales Tax -- This matters because you may be replacing a vehicle or RV and the tax must be paid for
registration.
In the US, domicile is essentially where you claim it and to where you intend to return (a "foreign" resident fishing
license, for example, casts doubt on your intentions...). Some states have conflicting laws in this regard, requiring domicile to be proved by actual residence of some sort, but these even conflict with their own voter
registration laws and may be overturned by courts (or not, depending on post 9/11 security requirements -- Who knows??).
There are organizations like Escapees, which will help you establish Texas residency/domicile and provide remailing services. There are also commercial services, principally I believe in
South Dakota, which will help you do the same there. I believe you have to be physically present in either place to start the process, DL photos, etc.