This is some information I put together from hours of reading post here on BITOG about air-cooled OPE.
If it were mine for winter I would consider GC, or Shell Rotella T6 5W-40, or Mobil 1 Turbo Diesel Truck 5W-40. I would prefer GC for coldest temperatures, but any of these would work. Shell Rotella is probably the lowest cost, especially by the gallon.
For mild temperatures I would consider the same oils, + Shell Rotella T5 15w40 (even lower cost than 6T), and mono weight Shell Rotella T 30wt, mono weight Pennzoil HD 30, or mono weight Castrol HD 30, or Mobil 1 15W-50.
For hot weather Mobil 1 15W-50. The recommendation for Mobil 1 15W-50 is from another person here on BITOG who lives in Florida. He said that he has seen several of his neighbors burn up engines on generators by using the wrong oil in the hot weather. He runs Mobil 1 15W-50 and has no problems with his generator.
Because Mobil 1 15W-50 is now SM rated I decided to go with Mobil 1 20W-50 that is still SL rated for hot weather. I would not run Mobil 1 20W-50 if the ambient were below about 60 F, and probably would only put it in if ambient were above 80 F.
I keep GC in the crank case of my 10 HP Tecumseh engine for my generator here in Pittsburgh PA. I also stock many quarts of GC in case of a long winter outage. Hind sight, a couple of gallon jugs of Rotella T6 5W-40 would of been cheaper. I picked up two quarts of the Mobil 1 20W-50 at Pep-Boys for a hot summer outage but have not had to use it yet.
I would also get in touch with the local Amsoil rep and get some foaming carb cleaner. About every 100 hours just before an oil change, use it, and run the engine for about 5 minutes to get it out of the carb and then change the oil. Also, put a new sparkplug in after that, carb cleaners foul plugs.
If you have a season that you do not use it be sure to either drain the tank, or add Sta-Bil to the gas, and then turn off the gas and run the carb dry.
I would change the oil every 25 hours with Shell Rotella, and every 50 hours with GC, or Mobil 1 15W-50, or Mobil 1 20W-50.
I saw something that said Rotella 10w30 does not have JASO-MA. You might want to think twice about using it.
Be weary of any oil not listed SL for use in OPE. The new SM oils have less ZDDP. Also if you stay with 30 as the high number, be aware that in general a mono weight 30 will hold up better in the high shear environments like air-cooled OPE.