One comment I received asked about timing and managing a family as a new professor. I'm going to be a bit vague about details in an attempt to conceal my identity. I have to say that there is no perfect time to have a family and if you wait for that perfect time, you will never have children. There are times when it is easier and times when it is harder, but have friends that have had children in almost any of those situations and you can make it work, and it will never be easy. I had the advantage of being on the younger side when I started my faculty position and thus I had the luxury of waiting a few years to get my lab up and running with a few graduate students trained before I got pregnant. Thus, there was not a total leadership void in the lab when I was gone. I also am fortunate to be at an institution that has a maternity leave policy for tenure track faculty that allows one semester's leave from teaching at full pay and a one semester extension of the tenure clock (this turns into one year in my department because cases are only reviewed in the fall). So I had my first kiddo pre-tenure and the second post tenure. My dream world goals were to get tenure and then have kids, but sometimes plans change in the real world.
As for timing in a theoretical world, I would say that is easier to either have your baby during your post-doc or after your first year on the job in a faculty position. The first year for me was really hard because I had all these new demands on my time and I had a hard time prioritizing them. After a few years I learned which things need to be done really well (grant applications) and the things that don't really matter so much. Now, when I'm strapped for time I know what things to let slide or do the absolute minimum acceptable effort to get by. Also, many things took me by surprise, advising weeks with 10+ hours of meetings, etc. Now I know when to expect them and I can plan accordingly. I also was busy trying to build my fake-it-till-you make-it image, meaning that I didn't feel like a professor so I had to think about how to act in a given situation very carefully and being pregnant/having a newborn during this time would have made it harder. For me personally, being pregnant really made me realize that I am biologically different from all the men in my department (duh!). As nice and understanding as many of them were (especially those who had young children) they still didn't know exactly what I was experiencing and my stomach was a glaring reminder of how different I was. That being said, sometime biology works in mysterious ways and I have had plenty of friends who started their faculty positions pregnant or with a newborn in tow and they have lived to tell about it.
When you are a post-doc you are younger (read can handle those sleepless night better?) and you have few responsibilities (meetings, funding deadline, etc.) which are pros for starting your family early. On the downside, you have less money for childcare expenses and you may have a more rigid experimental schedule that can easily be thrown out of whack by bed rest or a sick newborn. Your partner may have a more flexible job during this time and I know some people who work in shifts during grad school/post-doc to avoid childcare expenses. This is easier to do in grad school/post-doc when there are fewer meetings/classes during the day, however this may be very detrimental to your relationship with your partner.
During your faculty years, you will have better financial resources to pay for childcare and you will be the boss (sort of), so you may feel less guilty about time away. On the other hand, you will have more commitments - teaching, research, service, etc. that make it harder to juggle more limited time. You may feel more stressed depending on what point you are at on the tenure track and you may or may not get relief from teaching and other duties (depending on your university). If you are several years into starting your lab, you may be doing less hands on research, which could be good from a safety point of view and also allow research to continue (through your students) during your time on leave.
Each person's situation is different and it will be a big change for everyone. I never thought that I could leave work before 6 pm everyday without feeling guilty, but that's what time my daycare closes, so it isn't even a choice. One thing you need no matter when you have kids is a supportive partner. Starting thinking and talking now about ways you can share the load and what you can outsource (house cleaning or yard work?). In our house we divide the pick-up/drop off duty for daycare, the meals, grocery shopping, laundry, sick kid coverage (think about alternating days with key commitments - e.g. classes) pet care, etc. Somethings are hard to divide (being pregnant and lactating), so think about ways the other person can help pick up the slack. And finally, remember that we become much more efficient when forced to be, so you will eliminate many non-essential activities when you need to.
For me, I knew that I wanted kids and a faculty position so it was just question of when. Is it hard and chaotic? Yes! Would I trade it for a calmer life without kiddos? No way. They are glad to see you no matter what kind of day you had, no matter whether your grant was funded or your manuscript was rejected. And, they will always bring you back to earth by reminding you that they don't care if you are a professor or not, you still make the best human kleenex available (which might explain why I now wear very few non-machine washable items of clothing) and you can alway make the boo-boo better with a hug and a kiss (if only research problems were so easily solved).