RVs are rarely cost effective
If you are trying to be as cost effective as possible, then you shouldn't be looking at an RV at all. It will almost always cost more to rent an RV than it would to rent a car and stay in motels.
As far as renting or buying one, I doubt buying one would cost less. Not only would you have a huge upfront costs, with no guarentees to get ANY of it back (what you do get back when you find someone to buy it would likely be a lot less then what you payed up front). Plus, you'd have to deal with things like taxes, insurance, and licensing.
If you read the articles I cited, you'll get a pretty good idea of what your options are, including a leaseback option, which might be the best bet.