Yes, check the oil often.
Change it and the filter at around 1,500 - 2,000 miles to remove the break-in residue/debris. You can use synthetic oil right way ... but I wouldn't. I'd change the oil 3-4 times in the first 10,000-12,000 miles so using synthetic for these short intervals is a waste of money. You'll see no benefit.
Be moderate with use. Try to stay below 4,000 RPMs for the first few thousand miles ... without lugging the motor too much. Also, try varying the engine speed when it's brand new ... so avoid really long highway trips until you have 4 or 5 thousand miles on it.