lawnguy, you are looking for one definitive, perfect answer. Well, you aren't going to get one ... because it doesn't exist.
People, opinions and experiences vary. However, if you read and weigh posts in this thread (and others) you should be able to take away some very useful advice. There are lots of experienced users on this forum. I, myself, have about a quarter century taking care of OPE and I have not yet lost one due to an engine failure. Some are decades old and still running as good as new.
For OPE, many of us find the HDEO oils to be very good, economical choices. They are shear stable, have a strong additive package and are better able to deal with the byproducts of combustion than regular (PCMO) oils.
Some specifics:
There is no synthetic 15W-40. A synthetic HDEO in that class is a 5W-40 ... and there is at least a dozen of them in the marketplace. However, being in Florida, I do not believe the cold-flow properties of a 5W-40 will help you much. If you feel a 40 weight oil is appropriate, then a 15W-40 will serve you just as well for less than half the price.
Synthetic oils typically do not protect better in moderate applications. Their advantages include flowing better in cold temps and surviving tortuous high temps and super long oil change intervals (neglect). They are useful in some applications but not magic in all.
If your machine is brand new and tight, you're probably best off with a slightly thinner 10W-30. Just watch for consumption. If the consumption in the first 50 hours strikes you as excessive, consider moving to the thicker 15W-40. I prefer Chevron Delo and Pennzoil Long Life 15W-40 but all major brands are at least decent.
I rarely use pricey synthetics in OPE, especially engines without a spin-on filter. The oil fills up with debris and carbon and should be changed relatively frequently.
If it's a new engine, search for "OPE engine break-in" threads within this subforum. You should change the engine oil 2-3 times in the first 12 hours of operation.