We have not had a pool put in, but we did have ours redone recently. You should get names of people they have previously installed pool for, and go look at the pools. Are you going to do a color or just the standard shade? We went with a black bottom pool. Also who is going to do the start up? When they fill the pool the water cures the cement and it needs to have special things done to it for it to cure properly. I could not stand who did our start up. They were using a pool guy, well he was on vacation that week so the pool guy used someone else to cover for him.
As with any contractor you need to look that they have the insurance and the financial soundness that they are going to finish the job.
You should be able to get a good deal with they way things are, get 3 bids and let them pull the permits.
Scott