Welcome to the CRVL Forum
You may be able to find an automobile broker here who could find you a used Cargo Van with reasonable mileage on it that has served it's time in fleet service. Everything working and in good repair and road ready. This would be 5 or more years old and reasonable in cost compared to renting an RV. Probably more fuel efficient as well.
Below are a couple of websites of mine where I've detailed my practices for Van travel. The Conversion & outfitting of a Cargo Trailer 6 X 10 is still in the planning stage as I haven't yet acquired the Trailer. A few simple power tools and a long week end could make the Van Conversion. A time saver would be to purchase from a kitchen floor cabinet from a build supply recycle center and build the kitchenette out of it. (basically cutting a counter top for a small cooking stove and basin) Then you could find some inexpensive carpet piece to cover your floor. Then the other amenities could be found in resale shops. You may want water containers and ice chest as new items.
But this could put you on the road quickly and reasonably in cost. Once you set out you may secure an agent to sell your Van (with everything removed) on your return. This gives them some lead time to find a buyer.
You are more than welcome to view my two websites below. The first on making such conversions to a Van, and the second a Portal of handy information to use before embarking on a journey or while on the same.
One book I'd offer you to read before you arrive here was one written by William Leas. His book is titled "Blue Highways" and gets it's name from the secondary roads on the map being inked in blue. Seeing the USA from the Interstates doesn't provide a very good representation of the country side and more than limits the "motoring" experience. Least, in his travels, chose to see the country from these back roads and annotated his experience as a journal which became his book later. I recommend this book frequently here.
https://www.amazon.com/Blue-Highways-Journey-into-America/dp/0316353299
These are just some thoughts to offer you. All the best to you.