People will argue about this for months.
There are infinite brands of oil, with pricing all over the place, and they all have their fans, but any average oil is gonna be more than enough to keep your scooter happy for years. Following the maintenance schedule is WAY more important than what kind of oil you use.
This thread is a Motorcycle Product News story sort of confusingly mixed with POCphils experience as a scooter shop owner, but I think it's the best-researched assessment i've seen.
topic1375.html#16184
Note they suggest waiting until the engine's broken in to run synthetic. Amd most people agree you should stick with synthetic or dino so they don't mix, but even that is debatable (there are even mixed oils available).
Phil also suggests using 5w-40 instead of the PGO spec 15w-40 in cooler parts of the country (CHICAGO!). It's the same (40-weight) once the engine heats up, but the lower cold rating is better for colder weather.
I just buy it at any auto parts store (napa, pep boys, o'reilly's, autozone, etc) or Target or Sears. You don't need special scooter oil. It's nice to support your local shop, but I don't live near Scooterworks or Ace or Motoworks, so save cash on oil and save up for something nice.
Gear oil, again, just buy a decent brand. Sometimes our weight is hard to find at auto parts stores, but I bought a bottle at Walmart for $15 that will last me the rest of my life at 90cc once or twice a year.
Assuming you're talking 4-stroke here, 2-stroke oil has even more fanatics, but again, as long as you use a decent brand you'll be fine, avoid the weedeater stuff, but don't spend half a paycheck on the strawberry-scented imported "made just for scooters" stuff.