I'm kinda funny about my 2-strokes. I like to stick to the same oil the motor was broke in on.
But if you don't know what was in it, any TCW-3 oil will suffice. Costco has Quicksilver (Merc)oil for $11.79 a gallon. I've used that since 1987 without a problem.
If you switch to a synthetic, you might want to purge the old oil out of the system first. Some petroleum based oil isn't compatible with it.
one factor that should not be overlooked there is hard carbon oil and low carbon oil
make sure it has tw3 one the container.
the other is for engines that run hot- eg chain saws. and air cooled engines