We have sold via airstreamclassifieds.com (only handles Airstream-branded units) and bought locally via RV Trader.
In both cases we relied on bank transfers and a simple DIY sales contract we did via an online legal site (I forget which one, but there are plenty).One key thing we established via the sales contract is that we sold the unit where is, as is, without warranty of any kind.
We declined to accept checks of any kind for our sale, and did not want to deal with actual cash. That's why we went with bank transfers. The only legality we needed to worry about was a signed sales contract, bill of sale, and not letting them travel on our existing license plate. They had to provide their own.
With our purchase we transferred the money, got the signed title and keys, drove our existing vehicle to the nearby state licensing office, showed all the paperwork and transferred an existing plate we already had (from the previous RV) to the new-to-us RV we had just bought, had them record the title, and added the new registration sticker to the plate. Then we called our insurance company to add our camper van to the policy, attached the repurposed plates to our new-to-us RV, and drove it home.