Well, I think it's a crap shoot. In our public school, anyway, you don't even find out who the teacher will be until about a week before class. And, changing teachers is a Herculean effort and most parents who've tried say "don't bother". Can you tell we had a bad year?
But, if you have any input, I'd look for someone who is warm and sensitive over anything else. We had a cold fish for 1st who always looked like she had just swallowed half a lemon. Someone who really cares about kids would be top of my list.