You really can't go wrong with lawn mowers. Any oil filter will do there really is no wrong choice. Just find one that matches your type and size of the model Kohler engine you are using. It'll be located in the manual.
Kohler engines have there own oil filters. The filter is based on the model of the engine. The best way to get the filter is take the model number of engine to a small engine shop and get the correct filter for the unit. Replacing with the wrong filter may damage your mower.