I'd go with 10w-30 'dino' without hesitation esp for break-in and with your climate. By 100 hrs or so I might consider a 5W-30 if going to synthetic, perhaps a 5W-40 after 3k hrs. Really, the same with 'cheap stuff' if it makes API S'x' spec per the OM.
IMO frequency of oil change usually trumps choice of weight. Modern stuff doesn't always need 15W-40 with tighter tolerances or if low hours. $.02
I'm running Kawasaki engines on my z turns I've always run Kawasaki oil but in the pass seams like I start getting oil consumption after 600 hours had couple going Thur half quart day I've already got 200 hours on one 350 on one thinking about switching to full synthetic mint of waiting to later or mint not need to anyway
Thought on the matter I've had people tell me 2000 hours and no problems