Here would be my list of "immediate" things to do upon purchase (of any used rig regardless of seller):
1. Replace old tires ($1100 or so)
2. Have a mechanic do a basic check on the vehicle. Mine cost about $100. He checked brakes (including emergency brake), spark plugs, belts, lights, fluids, etc. - all the standard items. Replaced/repaired as needed (he deducted the $100 from repair costs).
3. Check the propane system for leaks, faulty regulator, etc. Not expensive to do and can save a life. I think I paid about $50 to find out I had a leak in the furnace and my regulator was bad (I had him shut off the connection to the furnace as I don't use it and replaced the regulator).
4. Depending on the age of RV, check the fuel lines for leaks. I had a full smoke test done - had a leak we couldn't find - maybe $100 or so if I remember correctly. All my fuel lines were leaking through miniscule holes (not visible without the smoke) and we replaced all 15 feet of hoses.
5. Check generator for proper functioning and leaks. I wouldn't spend money replacing parts unless there was a problem with them, but making sure it works and isn't spewing gas fumes into the house is money well spent in my mind.
Do those up front and you can prevent real problems.
You can sanitize a fresh water tank yourself (tons of posts on that). As others mentioned, the black and grey tanks don't need to be professionally cleaned just because someone else used them (did you have your sewer lines professionally cleaned when you moved into your home?)
On batteries, I wouldn't buy right away. First figure out if the one(s) already installed is sufficient for your needs. If so, then you saved yourself money on what you didn't even need. If not, then figure out WHAT you need and then select what to get (2 - 6v in parallel; 1 - 12 v; 2 - 12v in series; AGM, etc.).
I would also try the appliances, dump valves, etc. myself before taking off on a trip. Easier to deal with a problem BEFORE you're out on the road.
