Actually, almost any light weight machine oil works well. I typically don't even use after run oil unless I won't be starting the engine for a while. (Weeks.)

But I ALWAYS run my engines dry. Our fuels are hygroscopic, meaning that they pull moisture from the air. Leaving fuel in the engine will cause the internal components to rust or corrode.

It's also why you should not leave fuel in your tank, or your fuel jug uncapped.
Dennis-