I think westend and scbwr nailed it.
- I'd start with a safety inspection (wheels, brakes, tires, bearings, lighting, propane, etc.)
- Then begin looking for signs of leaks (check windows, roof and all sealant arount everything that protrudes through the top and sides of the trailer. Push on all walls to see if there's any unseen rot.) and other damage. I'd recommend resealing everything if it looks like theres any deterioration while you're up there.
- From there check the function of all appliances, water system, flush black/gray tanks, and sanatize water system.
By this point you should have a good list of To-do's yto keep you busy and hopefully there's nothing major. As the receipient of a trailer with water damage, I'd recommend resealing everything if it looks like theres any deterioration while you're at it.