Winston and the others know way more about these machines than I do, but I really like the Rotella 5W40 fully synthetic stuff. It's available for cheap in gallon jugs at Wal-Mart and the lighter cold weight lets my old batteries turn the machines over more easily. I was surprised; it made a perceptible difference, especially on the machines with tarry sludge masquerading as oil in the crankcase.
There is no difference in oil viscosity at operating temperature compared to conventional 15W40, and it flows better at low temperatures. I don't know of or perceive any downside for our purposes, except it is something like 4 dollars more a gallon. It meets all the requirements of 15W40 oils as well. I run it in literally everything I own with an internal combustion engine: motorcycles, tractors, pressure washers, push mowers and cars. I like it because I change all my own oil and it provides commonality. I always have oil on hand for whatever I'm working on.