When deciding where to cut my copper tubing, how deep (length) will it be once seated in the fitting?

Gatorbite and sharkbite are very similar, about 1" of your pipe will go inside the fitting. How the SharkBite Plumbing System Works SharkBitePlumbing.com

The fitting should have a tag on it that shows cutting and fitting depth. Mr. B gave you a good site to watch.