Pediatrician shopping

Brian and I are in the market for a pediatrician. We've met with two doctors so far and have appointments set up with two others. It's been a little weird so far.
I set up these meetings with the doctors (Brian was in charge of arranging day care tours and I took the pediatrician task...) but then realized I didn't know what we should ask them. We wanted to come across as informed and well-prepared parents-to-be, but the fact is we are going to trust what the doctor says on most medical decisions. And I don't think we'll veer from traditional medicine, and the standard pediatric recommendations, in most cases.
Luckily Brian found a site with some suggested doctor questions before we went to our first "interview." It suggested we take note of things like: friendliness of the staff, whether the office has a well and a sick waiting room for the kids, and what ongoing training the doctor receives. We also wanted to find out about getting same-day appointments, the options for after hours care and whether we would always see the same doctor.
The first doctor we met with was definitely strange. He was nice, but didn't really answer our questions. Or, in the cases where he did give us answers, it took a long time for him to get there. We met with another doctor this morning who was better. He was also a little weird — maybe it's a pediatrician thing since they're so used to dealing with kids? But we liked this guy better. He seemed to know his medicine and was willing to share life lessons with our kid. "Life isn't fair" seemed to be a favorite that he shares with children he treats. Brian likes the idea of having a doctor who can teach our kid a thing or two, or at least drive home some of the lessons that we try to teach!
We have two more pediatrician appointments in the next couple weeks. I'm hoping that we're able to click with one of the doctors and that will make up our minds. If not, I guess we'll go with the least-weird one.

P.S. I got some pretty good sleep last night, despite having to get up at 5 a.m. today to fill in on the early shift at work. I took a half-dose of Tylenol PM (just to make sure I actually heard the early alarm this morning!) and noticed a lot less pain when I had to get up and then back down during the night. It's amazing how much it helps to get some quality sleep!