I interviewed about a zillion providers when my first 2 children went to day care. Then, I opened my own childcare business for 5 years. In my humble opinion, I think your gut feeling is the most important thing of all. As you're asking questions, just keep looking around. Don't dismiss weird stuff that doesn't sit quite right with you. I had such a hard time when I was interviewing providers. There are a whole lot of people out there that just don't parent like I do and it was painful to imagine my baby/child going there. Just for a couple quick examples, once out of the corner of my eye I saw an elderly woman who worked at the day care, slap a toddler's belly because she was lifting her shirt up all the way. She said "don't show everybody that!" and gave her the slap. I also witnessed the owner of one day care practically dragging a toddler that was brand new to walking over to the lunch table. I didn't see one little toddler being held there, they were all drug around by the hand.
And the very worst one of all was a childcare provider who wanted to introduce my 11 month old to the 11 month old boy she already cared for. The 11 mo old was sound asleep in a playpen. Against my protesting, she went over there and yelled into that sleeping boy's ear "Bye Steven! Goodbye! You'd better wake up or we'll leave you! BYE!!" just to force him to wake up and meet my toddler. I practically ran out of that place. ~shudder~
I think you just have to keep an eye (& "gut" ) out for providers that really seem connected to their children- carrying the babies/toddlers, giving them all eye contact, speaking to them kindly instead of harsh and demanding, smiling a whole heck of a lot, responding every time a baby cries, not leaving anyone sitting around strapped into their car seats all morning (ugh, I saw that so commonly as well). Personally, I found providers that wore large amounts of makeup and jewelry a little off putting, but women in jeans and silly t'shirts so much more comfortable. Another personal thought of mine is that, when I would ask a provider why she decided to become a childcare provider (a very important question! ;) ), the answer "so I could be home with my kids" never sat quite right with me. Something more along the lines of "because I really enjoy children" or "being surrounded by all these goofy kids is so much more entertaining than sitting in an office!" with a nice big smile on her face is more my style. Someone who just "wants to be home with her kids" doesn't really give me the impression that she wants to be around my kid, y'know?
And of course you'll want to know if the childcare offers any sort of religious teachings so you'll know whether they're aligned with yours.
Hopefully, you will be able to find a provider that just really loves babies. I've always loved babies! I enjoyed carrying them around with me all day. I never had more than one young baby at a time and never used playpens at my home. I kept my business at full capacity those 5 years- eight children. I've been joking ever since that I've been just creating my own permanent childcare- I'm on baby #7 now.
This is entirely a matter of opinion for everybody, but I always preferred home based childcares as opposed to centers. I liked the homey feel and that they were usually much smaller groups of children than the centers. I liked that I could get to know all the other children there and the provider herself much better. In the centers, there were (in my experience) more people working there than I could keep track of. And I wouldn't even be introduced to each one. That made me uncomfortable- there's no way to get a gut feeling about someone you never even get to hang out with!
Anyway, I wish you much luck! It is no easy matter deciding who will be best to take care of your most precious treasure everyday! Trust your gut!