The insurance company's suggestions are probably driven mostly by cost, but should provide a reasonable starting point for assembling a shortlist.
If angieslist.com is active in your area, you will find some good info there. They have "Auto Body Work" as a category, and they post (and vet) reports from actual consumers. I had a new furnace put in recently, and found the $20 to be a good investment -- led me straight to a local company with a solid "A" rating and good reviews, which lived up to it.
Yelp.com is also of some value, though less rigorous.
At the very least, check out your candidates with the local Better Business Bureau -- might also look online to see if you have a state agency that fields consumer complaints.
Finally, a good auto body shop, in the area where they do the actual work, should look organized and clean (it's hard to do good paint, in particular, without that). They'll also be proud to show you some of the "after" examples they've got at the moment. Insurance work that has to move smartly along to get someone's commute car back into service is never going to look like connoisseur car-show work, but it shouldn't be sloppy looking either.
Ask how they check for damage related to the obviously crunched part, and what if it is not immediately apparent, and how they handle the billing for that.
Watch out for 'em deer! They can come out of nowhere, especially in evening and early night, and this is the worst time of year.
--Joe