For the initial startup on a rebuilt engine I would use a non synthetic break-in oil of 10w30 weight even if you have a roller cam, its to seat the rings properly as well.
Drain the oil after the break-in period, I know it cost a few bucks but I'm sure that new motor cost a pretty penny.
After that a 10w40 should be good.
On my flat tappet annual oil changes..... after I've drained the oil with the drain plug still open, I pour a quart of inexpensive oil right through til drained then close things up, new filter filled with as much oil as I can, screw on then fill crankcase to capacity.
The extra zinc & phosphorous probably doesn't hurt the engine. I've been using Brad Penn with no problems for years. I also add a little of this once in a while, good additive.
https://lucasoil.com/products/engine...e-tb-zinc-plus