Castrol engine oil. That's all I've ever used. Which is considerably less thick than your gearbox oil for a car. Been using that for years and never had a problem
I'd be wary around car oils. No matter how thick or thin they are. I'd rather spend the extra couple of quid on proper oil. I only say this as being stingy cost me some ££ in repairs on my clutch plates. If it was a dry clutch set up, it'd be completely different though.
Clutch plates are like £20 for an ebc set. And as said that's all I've ever ran and never had a problem. The only time you've had a problem with engine is oil is when you've used magnetec oil. I know this cause I've done the same and it causes the plates to slip. But swapped the oil over and it was fine. I ran magnetec for months with it slipping and when I changed the oil the problem stopped with no damage to the plates. Although I stayed out the band cause obviously it was dlipping