Q: I was thinking of using a synthetic oil
A: I don't think that bike qualifies as a crotch rocket unless that is a 2-stroke engine in the chassis? You could use synthetic oil, though its totally unnecessary unless you drive a lot of miles each year. Just make sure to get a good brand name oil. I'm using Mobil Clean 5000 10W-40 in my 2006 GSXR 750, it's supposed to be good for 5000 miles. I'll never ride 5000 miles in a year and synthetic is usually good for 10,000, but you should change the oil annually at least.