I use automotive grade oil. From years of motorcycling I do believe synthetic is far superior to mineral based. Synthetic oils are modified to better withstand high temps. High temps are quite common especially in air cooled engines. The only rating numbers that matter are the ones that indicate oil viscosity. The ratings are indicated as things like SD, SH, etc. They can be found somewhere on the bottle. Your owners manual will list them as well. As long as a few of those ratings on the bottle match those in the owner's manual, the oil is perfectly acceptable for use.
The reality is that most engines in just about anything are made better than they've ever been. Before my parents bought the Dixon, they had an old Snapper with an 8hp Briggs engine. That engine didn't have pressure lube. It didn't have a cast iron cylinder sleeve. The engine ultimately died on it. My parents didn't repower it because it was already too small for its job. Most of the newer engines all have much tighter tolerances, pressure lube, cylinder liners, improved carbs, better ignitions, etc. Oil is certainly a key element of longevity. Good design and build quality are as well. Whether you use Amsoil, Mobil, or whatever they sell for .99$ at the local gas station, you're probably going to find that your engine will hold up just fine.