I'd expect a call from an adjuster within 24 hours of filing the claim. You can take it wherever you choose for the repair, NW will recommend a "blue ribbon" shop near your location. These shops just make it easier on the adjusters because they use the same estimating software and usually agreed upon labor rates. Get a couple estimates, if you feel like it.
The shop starts on the work and determines it is worse than they originally estimated, they'll write a supplemental estimate, no big deal.
Both parties having the same insurance carrier, actually makes it a little smoother as it doesn't have to go to subrogation to get money back from the other carrier.