For my self propelled Deere mower, I use whatever diesel truck oil I can find on sale from Walmart.
I change it once a year, and the oil always comes out clean. I'm probably doing it too much, but for 3-5 bucks its good sense.
The Deere has a standard Briggs engine and takes 20 ounces of oil.
I have used 10w40 and 5w40 in Texas, we mow almost year round, sometimes I find myself doing a quick mow in January to clean up the weeds.
No smoke, no blowby, no usage and the Deere is about 8 years old now.
I think the most important thing is when we get into late fall, or early winter, I start running it on the expensive canned ethanol free gas from Home Depot.
That way I don't get any gelling or anything while it sits.
So I spend maybe 7 bucks and run it on canned gas a few times to circulate it through the system.
I throw a new air filter in the Deere about twice a year, as the dusty dry grass gets sucked into the filter quickly.