Getting a $5000 minivan and driving around as much as you are talking about will be a crapshoot. You might get lucky and have no mechanical problems. Or your could wind up with major issues.
But is probably the most economical way to go. With $5000 there really isn't a better alternative than car camping. Especially when that $5000 has to include the car. Now what you could do is get a motorcycle and little cycle tent trailer to pull behind it or a cargo trailer and put your gear there. Maybe every once in a while stay in a KOA Kabins or hotel room especially if the weather looks bad.
