Having spent 14 years in the parts business I had many occasions to make the body shop/new customer connection. Both were our customer. I stopped doing it because both end up pissed off.
Body Shop: keeps adding work but holds me to the estimate, car is worse than we thought, constantly here nit-picking, parts missing/late, keeps bugging me to finish it. Owes me money.
Customer: Taking longer than agreed on, costing more than agreed on, not the level of quality I expected. Doesn't return calls, why is my car outside???
Valid issues on both sides. Try to avoid them.
First and most common mistake is taking a car to a production body shop. Most are slow at this time of the year so they will agree to anything. If the shop hasn't done restoration work in the past they don't realize how putsy it can be. They take all sorts of ugly shortcuts; lap-weld floor pans, splice panels to avoid drilling out spotwelds. The instant they get some insurance work in your car sits. Sometimes parts are removed and later cannot be found.
Find a shop that has done resto work and talk to some former customers.
All shops have an "undisclosed damage" clause that you need to understand. No one has X-ray vision and all sorts of problems can show up when the quarters are removed or 3 coats of paint are stipped off. If you want it made right costs and time will increase.
Help yourself out-do as much of the grunt work as possible. Don't drop the car off with a full interior and expect them to remove/store it for you.
Don't expect any shop to finance your restoration. Space is always a factor and they schedule to maximize usage. Having a deposit is one way to ensure your car will be there on time. They have all had guys "change their mind" and go somewhere else. The instant it arrives the clock starts. The shop wakes up every morning and starts eating money.
Asking for money up front is also a character test for you. $1000 is peanuts in the hobby and you're already flunking. There won't be an insurance check and they don't know you. A small risk to get the relationship off on the right foot.
Good Luck!