For birds.. you want to make sure they are handfed/handtamed and TOTALLY weaned (Do NOT listen to any breeder that says you need to hand-feed yourself. Handfeeding baby birds is a complicated ordeal), banded, social and tame.
If possible, I would also go visit. Same things you would check for a dog breeder. Things are clean, animals well taken care of and VET CHECKS.
EDIT: just saw your post. A pet store I used to work with got birds through delta quite a bit. It's a pretty safe process.