That part about running out all remaining fuel is very important. If you choose to use after-run oil, any of the air tool oils are good. They contain rust inhibitors. For instance, Marvel Air Tool Oil is Marvel Mystery Oil with rust inhibitor added.
Another good after run oil is Rislone. I'm sure many others work, but I've tried these.
If the plane, or whatever vehicle, is going to sit for more than a week, I would suggest removing it from the vehicle and removing the backplate to check for any remaining fuel, then apply an after run lube. Your bearings will thank you.
George