Mail - sign up with one of the many professional mail forwarding companies. this should also be coordinated with your choice of domicile state, if you're planning to change home states while fulltiming. another option available to some, is to use a close family member to receive & forward your mail.
Medical - this depends on your insurance coverage & health issues. some have HMO type coverage which requires them to return to a specific area to get "in network" treatment. emergencies are usually covered anywhere.
Those with PPO plans or federal medicare or VA can get covered treatment anywhere in the country.
Those with ongoing health issues may prefer to return to the same medical providers each year for followup. Those needing only routine checkups can select a doctor anywhere along their route.
Guns - no problem carrying firearms in your vehicle, if you comply with the federal requirements for transporting firearms. Once you stop for an extended stay in a state, then you need to comply with that state's laws, which are available online from several sources. Many of the western states where gun regulation is more limited, allow open or concealed carry in your vehicle with no permit, a few even allow loaded firearms in your vehicle. The state by state vehicle transport rules are usually different than the carry on your person rules. So the CCW is usually needed once you step outside your vehicle, not always required while in the vehicle. (western states)
these rules also change frequently, so keep up to date. I carry 2 pistols, a lever action rifle and a shotgun in my motorhome, almost everywhere I go. I participate in firearm competitions all over the western US.
Canada & Mexico - stay out if you prefer to carry firearms with you; or find a shop near the border willing to store them for a fee. one loose bullet found in your rig can send you to a Mexican jail.
Jim