Really anything you have on hand will work, I have a Troy Bilt pushmower with the gcv160 and mostly run 5w30, I currently have PP in it right now but mostly in my pushmowers I use Delo XLE 10w30 and you used to be able to get it for a great price at Walmart but it's getting a lot harder to find and the cost has increased.
These are a fairly decent motor but they do have their issues, plastic cam gear that's prone to breaking and I believe the valves can get sticky which is more or less why you would want to run a synthetic oil.