You did not say if you have RVed before or not. I will take it that you have not rved before. With that in mind I would search out a certified RV inspection service in your area. This would not only give you peace of mind but a good starting point for maintenance.
The list you asked for will go on for ever the good folks on this forum will provide great information.
You will need to check everything from tires to caulk. Leveling jacks to tv antenna.
When I purchased my 07 meridian I took it to a shop that deals with rvs and busses for a look see. It turned out need front wheel bearings. The cat c7 needed air dryer. My point is a certified rv inspector would have found these items and saved me some time and money.
When you say "winter proof" theres really not much to do as the current owner should have winterized the water system already. If you mean make it livable in the winter good luck. You most likely will need to get an adapter for the propane so you can get a larger free standing tank. Some type of insulation around unit.
These links may help you down the road
Good Luck and safe travels