Bigbird is correct and gave good advice.
Scooters inherently run pretty high/semi constant rpms due to the CVT. Although not a shared sump, it still takes it's toll on most oils in a short time. This makes them the perfect candidates for HDEO's - as they are very tough and very shear-stable by nature. As another plus, they're great cleaners and will keep one clean at the same time.
Something about OCI's - you might want to change oil a couple of times relatively soon. You would be very suprised to see how much metal comes out initially (metal slurry) - looks like glitter in the sunlight. Whether left over from initial assembly or initial break-in doesn't matter. Those small flakes of metal are causing unneeded wear that you don't want. It needs to come out, since most scooters don't have an oil filter - just a gravel screen. Scooters are also great candidates for Magnetic Drain Plugs too.
I change my oil in a new scooters at 30, 60, 100, and 250 miles (I know but it doesn't take much oil anyway) and there is always glitter in the first 3. Sometimes the 250-mile OC is unnecessary but it's the only way to be sure.
If yours is a Chinese scooter - Do not run one long at all on the shipping oil (they call it break-in oil) - it's junk and will shorten overall engine life. It is very cheap and incredibly poor quality - all it does is keep one from rusting during oversea's shipping. Change it out immediately.
With that being said, I change oil in mine every 1,000 miles (once again no filter) reguardless of what my manual says. On my Honda Metropolitan, Honda recommends a 2500-mile OCI - nope, not in mine and not without a filter!
I usually run a steady diet of Rotella T 15w40 for Summer and Rotella T6 (5w40) in the Winter. These are great oils at a good price and available about everywhere (wal-mart). Technically, the T6 is considered a synthetic, but I use it in cold weather for easier start-up.
Speaking of synthetics, no problem using them at all. I would just wait until my first couple of short OCI's are done - no need to waste it. Actually, you can go ahead and use T6 year-round with no problems at all, I just have a few gallons of Rotella T stashed that i'm going through right now. Performance-wise I really can't tell any difference between the two though.
Hope this helps. BTW, is it really 500cc's or 50cc's?