I would run 10w30 which is what kohler recommends. Briggs recommends 5w30 synthetic. I have a kohler and ran rotella 10w30 for 20 hours.....came out black and thick.
I now run Amsoil Small Engine Oil which is designed for small engines. Comes out looking a lot better than the rotella I was using.
If I was using rotella again I'd use the 5w40 full synthetic
2010 Toyota Camry:
Amsoil Signature Series 0W20
Amsoil Signature Series Trans Fluid
Amsoil ATF Power Steering Fluid