Get em early, use a spoon to remove an inch or two of soil and cut or snap them off. I'd say nothing taller than 6" is worth bothering with but shoots fatter than 3" might be an exception,
To peel slice in half lengthwise and bend the half back, the edible part will pop out and the leaves and sheaths will remain behind.
Before cooking try some raw, the bitter types might need a parboil and water change but if you like them raw not much else is needed.

What kind of shoots could be big enough to harvest in NH?

An unknown assumed to be Phyllostachys that I've had for about 15 years, 5 at this location. Gets about 3/4" diameter for me here. Not large enough to bother otherwise, but shoots that invade unwanted areas get cut, and rather than go to waste may as well serve a purpose.