Welcome. We did something similar to what you are describing. We're not quite finished, but we are on the road now. I blew past $5k a loooong time ago. I suspect you will too, but with some research and some luck, you can probably do things in stages to make it work.
First thing is to address anything structural. Frame and subfloor. I know you said the subfloor was good, but it's worth another look. It will never be easier to fix a bit of subfloor than it is now. If the subfloor looks questionable somewhere, there's a good chance the frame under it has some rust that'd be worth looking at. Very common for several outriggers to be busted and in need of welding repair.
Axles. How do yours look? If they're original, they most likely need replaced.
Leaks. Get a suction cup and a bottle of Captain Tolley's, and check every single rivet. If the suction cup sticks, the rivet is good. If it doesn't, hit it with the sealant until it does. Check the sealant around your windows and doors. It's probably due to be dug out and replaced. Check the rubber gaskets on your plumbing vents. They're probably cracked and leaking. Check all your window and door gaskets. They probably need to be replaced.
Check all your appliances and systems for function. Original plumbing systems of this vintage tend to be a patchwork of questionable repairs. Do you have a propane alarm? You need one. And a fire extinguisher.
What kind of fridge do you want? If I had to do my reno again, I'd seriously consider a vitrifrigio/danfoss DC compressor fridge. Works great with a serious solar system. But then again...
Your budget is probably going to preclude a serious solar system. I suggest installing a solar combiner box on the roof and run adequate sized wires to wherever your solar controller is going to be. Then you can easily add the panels and controller later when you have the money. Build a big battery box and put a regular sized battery in it for now, so you can get a bigger battery bank when you have the money. I'm running 200 watts of solar and a 100AH battery, and it's just enough to get by with some hand-wringing when we have two rainy days in a row. I have plans to add 2 or 3 more 100 watt panels and buy a bigger battery when I can.
Do you want an inverter? I bought a big honkin' inverter that can run anything in my Airstream, and to be honest, I mostly use it to run the coffee grinder. You can do most everything on 12V
if you plan it out. Get car charger for your phone and laptop. Get a 12V
television if you want one. Convert your lighting to LEDs so your battery lasts longer.
I guess that's enough to get you started. Lots of folks have blogs on their renovations, and they're worth checking out. Mine is in my signature. Spend some time on the forum reading all the reno threads, and you'll get an idea of what you need to do. Post pictures on your own thread and ask questions along the way. You'll get a lot of help.