Always consult your owners manual as it is the final word for your engine. But if you no longer have your owners manual or are just looking for a bit of clarification, this should help.
The use of a quality major brand oil is best but
as my good friend "Doc" says, any brand of clean,
fresh oil is better then old dirty oil.
Change your oil according to your owners manual. For engines without an oil filter this usually will be every 25 hours of run time. Engines with an oil filter will have oil change intervals of somewhere between 50 and 100 hours. Engines used in very dirty conditions, such as roto-tillers, should have their oil changed in half the time. For low hour use engines, change the oil twice a year. Combustion by-products that get into the crankcase create acidic properties which need to be removed to prevent internal tooth decay.....Bet that caught you off guard. That's about the simplest way I can think of explaining it. Old oil has some nasty stuff in it which is harmful to not only humans but to your engine. If you don't use your engine enough to change the oil at least twice a year in hour terms, change it anyway.
When ever you check, add or change the oil, be careful to clean the access plug, cap or dipstick comletely. Just one grain of grit dropped in the engine can be caught up in the piston or bearing and cause major damage in a very short time.
For warm weather operation, use a single viscosity 30wt oil. Multi viscosity oils are ok but make absolute sure that you change oil on schedule or sooner. Muli-viscosity oils tend to break down quickly in air cooled outdoor power equipment because the engines run so much hotter then your car.
If your engine is run in ambient temps below 40° the use of 5w 30 or 10w 30 is preferable. It allows easier starting when the engine is cold and the ambient temps will allow the engine to run cool enough not to break down the multi-viscosity oil at a accelerated rate.
For snow blowers or other engines that always run around the 0° mark or below, most engine manufacturers are now giving the thumbs up to use a straight 5w or 10w synthetic oil. This again aids cold engine starting and provides protection for the engine. Don't use straight 5w or 10w much above 0° as the oil will be too thin once the engine warms up.
As for synthetics in general. Most engine manufacturers now allow it's use across the board as long as you use the right viscosity for your operating temp. However you should still use a petroleum oil for the intitial oil change on a new engine which is 5 hours of run time. The obvious drawback to synthetics is the cost. Your oil change intervals must remain the same as the combustion deposits still are present. The synthetic itself doesn't break down but still becomes contaminated and needs the same scheduled changing. The question becomes, does the cost of the synthetic out weigh the savings in extended engine life? I don't know if anyone has as of yet, done a thorough test to determine this. For now, it's a decision you'll need make. Bob........