Now, don't take this the wrong way but (afterall) it is their currency so you should use it for your everyday needs. Either changing at a Cambio or using a Jamaican-dispensing ATM would be my recommendation. Having a few small US bills for "special" tipping is a good idea as well. My advice is to get "80:1" ingrained in your mind. It is not exact but gives you a ballpark reference point to deal from. Divide a Jamaican price by 80 (roughly) and if you wouldn't pay that in US currency, don't buy it. Simple as that. I see a meal for $800 J and immediately know it is close to $10 US and from that I can make my decision more easily.
I find it is best not to bring large bills to Jamaica but others may differ on that advice. The ATMs make it so easy to get a measured amount of money when you need it without too much hassle and it doesn't give someone an opportunity to steal from you too easily as well. Travelers Checks are good as well. Better to be safe than sorry.
Peace and Guidance.