***caution*** opinion ahead.
If you want to use synthetic oil go ahead but...... synthetic oils used in automobiles allow those engines to longer between oil changes before the base oil starts breaking down. Synthetics don't offer better lubrication than mineral oils. They take heat better and last longer. All that us not all that helpful in a small engine unless you want to go long periods between oil changes which may not be the best thing for small engines.
Oils designated for automotive use have little to no ZDDP in them per government rules. Oils not intended for automotive use can have higher levels of ZDDP. ZDDP is an anti wear additive added to oils to help with wear on flat tappet cams in automotive engines with high valve spring pressures. Small engines have much lower spring pressures. Most you can compress with fingers. ZDDP additive is not that important in a small engine vs. Something like a high revving V8 with a flat tappet cam. Use whatever oil you want and have confidence in but a non synthetic SJ rated 30wt or 10w30 without ZDDP package will work fine. The most important thing is not how expensive the oil you use is but how often do you change the oil? The stuff that turn the oil black is the same whether synthetic or non synthetic oil is used. The more often you get that out or the engine the longer the engine will last. You can leave oil in too long but you can't change it too often.
I've been studying engine oils for the last 15 years. This jives completely with my understanding. Thanks.