Tom has it right about oils for the older engines. From the Kohler site:
10W-30 (Command Oil) is recommended for Command, Courage, Command PRO, Command PRO CS, Triad OHC, and Aegis engines for temperatures above freezing (32°F, 0°C). SAE-30 is an acceptable substitute if temperatures are above 50°F, 10°C. K-Series and Magnum engines should use SAE 30 (Magnum Oil) above freezing. 5W-20 or 5W-30 can be used in all engines when temperatures are below freezing. For more complete oil specifications refer to your owner"s manual. For optimum performance, Kohler"s special blend oils are available from your KOHLER dealer.
Synthetic oils meeting the classifications listed in the owner"s manual may be used, however oil changes still need to be performed at the recommended intervals. To allow the piston rings to seat properly, Kohler recommends operating a new or rebuilt engine for at least 50 hours on standard oil before switching to the synthetic oil.
In my (slightly) opinionated opinion, dirty contaminated oil of the correct type is worse for your engine than the wrong type but clean oil. My experience working on others small engines is most worry lots about using the right oil and very little about keeping it changed at 25 hours. Oh they say they change it, but the insides of their engines say different,,,