I buy the little, 1 gallon size, synthetic oil for my chain saw, leaf blower, weed whacker. Its not the cheapest but with todays crappy gas, why add another reason for those little motors to fail.
My dealer also suggested to drain the gas out of the tank if the machine isn't used at least a couple times per month. I agree since its usually the reason I have to take it back to him because it is running crappy. Mine all have primers that really push the old gas out of the carb, not just prime a full bowl so I get newer gas in it.
Chain oil is for chains not motors and vice versa. Its a real sticky oil, almost like honey.