KayBayDog gives good advice. Do your homework. Do not rely on scuttlebutt and jail house lawyers, you could get your okole in heap big trouble. Lets see:
Usually, auto insurance rates are based on where your auto is and where it is being used. If your car is registered in,say, Alabama (low rates) and your auto is in New York, very high rates, you will pay the New York rates. If you do not declare that your auto in now in New York and not Alabama, hey you have no insurance! Does this mean all insurance companies, how could I know? You gotta find out.
State of residence is usually where entered service, But you can change it. I recommend changing it to a state that payes no income tax. But you gotta find out more about that, for example, Florida has no income tax. It does tax, heavily, intangibles such as stock. You gotta find out from your PSD what you need in order to change your state of residency.
Soldiers and sailors act prevents states for taxing non-residents, prevents states from requiring you to register your auto, to have same address on drivers licenses and registration and such.
Back to the auto. If you do decide to register your car in VA, they will probably charge you tax on the value of the car. That you paid tax in your home state might not make a difference. Some states do not have "sales tax" for autos, they call it "excise tax". Thus Florida for example may say they will exempt sales tax if your can prove you paid sales tax in your home state, you, only to find that Maryland calls it an "excise tax" and thus you are stuck with Florida sales tax.
Know before you jump.
And another thing: You Marines stop gathering in the passageway and blocking the dog gone ladders! j/k.