Go on over to cheaprvliving.com for much good advice on living cheaply.
In your shoes I would look for a trailer & tow vehicle. That is by far the cheapest entry point to RV life. It's easier to buy a dependable used tow vehicle than a dependable used motor home. Something like a F-150 and a smaller used toy hauler that you can customize to your needs would be a good choice for a single person.
I would also look for some supplemental income. $2K/month isn't much.
You need an exit strategy. What if you get tired of it, or have medical reasons that you can't do it anymore? You need enough income and/or savings to get set up in a place to live. Don't put ALL your savings into the depreciating assets of a RV and tow vehicle.