Hi and welcome! There's a good
thread on homebirth resources here, and it's also very helpful for preparing for birth center births. It includes things like interviewing midwives. You could also post in the
New Hampshire forum asking for recommendations for specific midwives or centers.
As far as safety goes, have you seen "The Business of Being Born?" That's a great introduction to the topic. Also, "A Thinking Woman's Guide to a Better Birth" is a good overview. I also really liked looking at professional studies that examined the safety of homebirth. One of the biggest and most recent was
Outcomes of planned home births with certified professional midwives: large prospective study in North America . That shows that for low risk pregnancies attended by a trained midwife and with procedures in place in case of transfer, planned homebirth is typically as safe as a hospital birth and with much lower rates of harmful interventions. A Canadian study that came out just a couple months ago saw similar outcomes.
That's a great interview list that Jecombs has.
As far as your questions go, hospital transfer is mainly going to depend on how close your home or the birthing center is to the hospital. Very few transfers happen in ambulances with sirens going -- it's more frequently getting in your own car and driving there at a leisurely pace.
Post birth infections isn't going to be on the top of the list of concerns, but that sort of falls under the general banner of post-partum care. You'll want to know what the schedule is for seeing mothers after the birth -- it's typically at one day, three days, one week, two weeks and six weeks.
You would want to ask tough questions -- have they ever lost a baby or a mother, and under what circumstances; have they ever had a bad birth outcome; have they ever had a lawsuit; what do they do in the case of emergency transfers.
The one thing about the really long list of questions is that you have to know what they mean for the answers to be significant to you. That's where just getting really educated about the birthing process is helpful.
Good luck -- it's a big learning curve, but it's so worth it. A lot of women spend dozens of hours researching strollers and cribs -- I think it's so much more important to do that research about your own body and birth.
ETA
Two more things: Like Meg said, it's really ideal to be able to labor
and birth in the water. Some places will let you labor in the tub until your water breaks, but if your water breaks at the start of labor, you're SOL.
Also, I know you said you're interested in a birthing center. And free standing birthing centers can be a great choice for a lot of reasons. But in terms of safety, unless your home is very far from the hospital, there tends to be very little difference birthing in a home or birth center. I've actually heard birth center births described as "homebirths you have to drive to." Midwives typically carry all the same medical equipment (pitocin, oxygen, etc) to a homebirth that they would have at the birth center.