You choose the body shop, don't let them tell you who is gonna fix it. Let the shop owner negotiate with the insurance company, and tell them OEM PARTS ONLY!!!
Even tho it doesn't look like a bad hit, make sure they send it to alignment, make sure everything is still square and running true.
Adjusters deal with fresh meat every day, they're trained well, "Oh I'm so sorry about your loss, you just sit back in your nice rental and we'll take care of everything." (even tho we're going to use our preferred shop, they're gonna use LKQ parts, and you'll never know it because you trusted us, and that was your first mistake)
Let the shop manager kiss their @ss, (sorry Rallysport, but you knew that when you took the job
) you be a prick (in a nice way) about getting it done right. Ask the shop if they warrantee their work and for how long, it's mostly for protecting you from chipping peeling paint, but if it's prepped right it may outlast the factory paint.
Having said all that, don't look over the finished job with a magnifying glass...The paint should be (mostly) blemish free, closely matched and blended so that a picky painter would say it's a good job. All door gaps should match and be even. 4 wheel alignment should be within spec.
Adjuster: "It wasn't hit hard enough to cause alignment problems."
You: "Well, check it anyways and make sure it's right, because I'm going to have it checked after it's repaired, and I expect it to be in spec.. (Why? because I don't trust you)"
Get the idea I don't trust adjusters?