Oil is good for a motorcycle. We can start there first.
So, a good quality oil is just fine. 10W40's are good. I'll usually lean toward a 15W40 because since the numbers are closer together, it has less of an additive package. In the warm months, I'll usually use a straight weight, like an SAE30. Little heavier, but good protection after shut down.
I like to check the API ratings on oils. I look for API diesel ratings...CD, CF4. Diesels hammer oils a bit more that a regular engine, so these oils don't shear so bad.
I like Shell Rottella T. Kendal is good, but now owned by Pennzoil, which I refuse to use. The former Kendal SAE30 has better film strength than most synthetics.
Will a synthetic offer more HP? Can't say that I've really seen it.
I did have a petroleum based oil made for myself that was fortified with Castor, the ultimate lubricant. It was an SAE10. Seemed to work really well, but the castor lubricant is rather dirty. Just the way castor is.