$2,000 is a bit optimistic. You'll need new tires out the gate most likely - that's $800 to $1500 right there. A new fridge can run $1000. A rebuilt carburetor - $300+. A rebuilt engine $3,000+. Smaller stuff adds up.
When I bought my clipper, right off the bat I had to replace all 6 tires, replace all the fuel lines, repair the emergency brake, and replace other hoses and belts. Within the first month, I had to replace the converter. The first time I tried to dump the black & grey tanks, the valves got stuck (rubber had deteriorated and got stuck in the pipes) and I had to have the pipes cut to get the gaskets outs and put back together. American Clippers are quality rigs - very well built for their age and mine was in good shape. But its 40 years old. If I were to live in it full time, I would have had to also repair/replace the furnace (in my situation, I just closed it off from the propane and use a Mr. Heater Little Buddy for heat the few times I need it).
My point is that $2,000 isn't a lot for repairs to make an older RV something dependable in which to full time. And if you can't do the repair yourself, you don't have a place to live while it's being fixed so you should have some funds set aside for a motel room, etc. in such a situation.
Also, depending on your income, you'll need a regular infusion of cash for new things to go wrong at any moment. With an older RV, anything can suddenly fail at any time. Living in it full time, you'll have to be able to fix those things asap rather than wait until you save up the money.
I would say, wait until you save up $25,000. Put $10,000 into the purchase; $3000 for the tow dolly and solar/battery system; and the rest for repairs as needed. Then each month for as long as you own it, put away an additional $200 towards the repair fund. If you're lucky, by the time you want a change, you'll have thousands saved up. Otherwise, you've got $12,000 to put towards repairs - both initial issues and emergencies. Each year, you'll have replenished your repair fund by $2,400.
1975 American Clipper RV with Dodge 360 (photo in profile)
1998 American Clipper Fold n Roll Folding Trailer
Both born in Morgan Hill, CA to Irv Perch (Daddy of the Aristocrat trailers)