Air temperature will determine the weight of oil and you will want a small engine oil. The colder the air the thinner weight oil you will want to use. If you live in a medium type climate a good 30 weight oil will do just fine. Any big box store will carry what you need.
The answer to this can depend on the size of the engine. You want to check your owners manual or research the manufacturer's model on the Internet to find out what exactly they recommend for thickness and viscosity.