Too much depends on your circumstances and the laws of your state of residence; therefore, I recommend contacting a local TN tax lawyer and then contact Bennett Law Offices in Missoula, MT for their evaluation (usually no charge). I believe it costs around $1,000 for Bennett to set it up, with a small annual fee thereafter. In general, a motor vehicle must be licensed in the state where it is primarily garaged, so LLCs work best for fulltimers that don't spend much time in any state.
I'm a MT reident, and my wife has a MT LLC for her business (corporate recruiter). Our vehicles are registered in our names in MT, not through the LLC. A MT LLC costs $50 initially (if you file the easy paperwork) and $15 annual fee.
MT has no state sales tax but has some local sales taxes on lodging, resturants, etc. No motorhome registration (tag and title including all annual taxes) costs more than $300 no matter how expensive the rv. Trailers, powered watercraft, motorcycles, and cars/trucks 11 years old or more can obtain a permanent tag with no additional fees (except watercraft).
Do your homework well, or you may have serious problems, but many rvs are legally registered to a MT LLC.