I'm almost positive Honda spec's 10w40 for their machines, and I seem to recall they specify a lower viscosity for winter months.
I've heard to stay away from synthetics, as it can affect the oil-bath clutch in the transmission, causing them to slip, but I know Amsoil makes a synthetic 4-stroke motorcycle oil, it might have the right friction modifiers to keep from burning out the clutch.
Any brand name petroleum based oil should be fine. Can't say for sure on the Synthetics.....