It'll actually be more protected with regular car oil than with wet-clutch-type motorcycle oil, because of those friction modifiers that can't be used with motorcycles that have wet clutches.
The general consensus is that diesel-rated oil is better, since it has the detergents and buffers in it to keep the oil clean and un-acidified. Our scooters are somewhat akin to a diesel engine in terms of quickly polluting the oil.
And a diesel-rated synthetic oil would be best of all, of course.
When I was breaking my scoot in, I used 15W-40 dino oil for diesels, and changed it at 50, 100, 200, 400, and 800 miles, then every 600 miles after that. After break-in, I switched to Royal Purple 15W-40. You can greatly expand the life of an engine by frequently changing the oil during break-in. I *should* have changed the oil at 25 miles, but I went for a ride and went right past 25 miles, so I figured I'd do it starting at 50 miles.
Don't buy into the hype of using thinner oil as a means of "gaining a fraction of a HP or MPG"... the thicker oil provides a wider safety margin in those moving parts that might just touch (and gall) with a thinner oil. So even though Kymco has stated that my scoot would be OK with a 10W-30, I stick to what was originally specified for it, 15W-40. And that becomes even more important as the scooter ages and clearances in the engine open up a bit.
At 6229.8 miles (I went 29.8 miles past the scheduled 6200 mile oil change due to too much other stuff going on at the time), I started three courses of treatment with LiquiMoly Ceratec. I put 1/3 of the can of LiquiMoly Ceratec in at the next three oil changes. I can't say there's been an improvement in fuel mileage, because there hasn't, but there was a slight power boost that allowed me to increase my Dr. Pulley slider weights from 16 to 18 grams with almost no discernible change from what stock feels like without the Ceratec (it actually pulls a bit harder to top end now than it used to without Ceratec and with the lighter sliders). And a bit of a boost to my top-end speed, too, although that just tends to push me into the rev limiter more easily (and it's already too easy to get there).
I've been itching to try out the Royal Purple 15W-40 with Synerlec (some sort of additive, I can't find much info on it, though)... apparently it's good for engines that don't have a roller type valve train. It's hard to find around here, though.
As for the gear train, when I was using the factory-specified gear oil (75W-90), I kept noticing lots of 'glitter' in the gear oil when draining it. I went to Royal Purple MaxGear 75W-140 with Synerlec, and now the 'glitter' is gone.