other insurance company just accepted full liability Yay!

First let me introduce myself,

My name is Jack and I'm no stranger to the industry but am to your website,

i used to work as an agent for 21st Century/Farmers, So I am very happy to have stumbled upon your website today.

I was recently in an accident relatively minor but my car ended up taking more damage than the other vehicle.

So after a slight off put experience from the other policyholders company, I am pleased to say that they just accepted full liability after my constant hounding in making sure things were getting done.

The accident occurred Thursday and was resolved Monday after i got the police report and sent it over to the insurance company.

My question for you guys is, The lady I spoke with who told me that they accept full liability asked if I had a body shop in mind yet and I told her no not yet. She told me about the preferred shops and blah blah, she said that I'll have to meet with their claims adjuster and they will cut me a check for the damages.

So what do I do? Do I get an estimate first from the shop I would like to take my vehicle then present the estimate to the claims adjuster or vice versa?

My only main concern is them "claims adjuster" estimating my repairs to be much less than the body shop I choose to go to.