New Growth...what to do?

We've been getting some odd spurts of relatively warm weather here in the NW. I went out to check my hops to see if they were ready for pruning. To my surprise, I found new branches coming off the vines that looked nearly dead from a distance. I have these new branches on several plants. Also there are numerous shoots breaking ground.

How should I address these two issues? Leave the new branches till they die back? Cut/pull the shoots or let them be for now?

I don't know about the 'branches' you're talking about but if what you mean by 'new shoots' look like the pictures below, that's normal. Some of the buds that form on the upper portions of the crowns in the fall can be pretty big. These will be the first ones to take off next spring.

I'll double check on the buds, but to my recollection they appeared to be shoots breaking ground.

Sorry, the "branches" I mentioned are new sidearms growing out from 4-6' up the main bines that had gone all yellow and brown.