I have a metal shed I'm going to run electric to. I'm going to install 2 LED overhead strip lights and a duplex receptacle. Other than the equipment ground I'm running with the hot and neutral (grounded conductor) from my house's main panel, should I also drive a ground rod or two at the shed and bond it to the equipment ground?
This sounds suspiciously like a do-it-yourself type question. If you are a do-it-yourselfer we are not allowed to help you perform actual work, but this seems more on the order of a request for information which they sometimes allow from diyers.
The answer to your questions can be found in article 250. The answer will change based on whether you are running a feeder or a branch circuit out to the shed. A feeder would require a grounding electrode system at the shed, while a branch circuit would not. You have not specified which you have.
A moderator may ask you to update your profile with your profession so you might as well go ahead and do so.