I've used synthetic oil in every engine I've owned since 1982 with zero problems. Break-in is done with specially formulated break in oil (made by Optima, Driven) after a couple of hundred miles oil is changed to synthetic (Amsoil, Optima, Driven) oil formulated for flat tappet cams for the cars that have flat tappet cams. I use Wix filters or Wix racing filters for the high rpm engines. If I wanted to use a conventional oil it would probably be Valvoline VR-1 for the hot rods. The viscosity of the oil is determined by the rod and main bearing clearances for the hot rods or manufacturers specifications for small engines. I also use synthetic 2 cycle oil in all the yard tools.
The oil in everything is changed once a year regardless of mileage, for the reasons stated in a previous post. I gave my old JD riding mower to my son, it is starting it's 32nd season on the original engine. The Honda walk behind mower is also starting it's 32nd season with the original engine. The Stihl weed eater, edger, and blower, are starting season 25 with original engines. I've owned several vehicles with 130K + miles that used no more oil when I sold them than when they were new. My truck has 130K miles and uses no more oil than normal.
Some differential do not like synthetic oil. I've heard True Track and Torsion Gleason are two of them but I don't have any experience with them. I do have experience with Ford traction-loks (8.0, 8.8, 9.0), Strange, and Detroit lockers. The synthetic (Amsoil, BG Products) work well in those applications. MANY years ago when I was attempting to do some road racing, I burned up two sets of Richmond differential gears. Used Amsoil the next time and never had anymore gear problems.
I also use synthetic (Amsoil, BG Products) in manual and automatic transmissions with no problems (top loader, T5, TR 3650, MT-82, C6). I do tend to use the transmission fluid specified by the manufacturer for the newer automatic transmissions. These are just my experiences with synthetic lubricants. Chuck