Regular car oil doesn't have the stuff needed to keep wet clutch lubed like it needs
Just make sure the oil rated "JASO MA" or "MA2".
Synthetic or conventional is up to you.
I read somewhere that the "MA2" rating is for engine exhaust with a cat and O2 sensor.
And I think the synthetic lets the clutch slip more than conventional. If there is a lot of miles on the clutch with conventional oil. Then switched to synthetic. The clutch is more likely to slip.