How can I trust a transmission replacement diagnosis?

We had a car towed in to an auto repair place after it started stalling and lurching terribly. They said there was no transmission fluid (had had damage to transmission due to some kind of impact), and that transmission needs to be replaced. How do we know this is the right diagnosis and fix, and can I trust them to do transmission work (Goodyear place)? (They have a list of other things they have found need repairing; are supposed to call me tomorrow when they are completely finished going over the car, with a full list of things that need doing, but the transmission is the main thing I am worried about.) This is the first time I have used your service; will gladly make a donation the next time around if satisfied.
thanks