What sort of formula should I look for for a very new newborn that doesn't promote constipation?
Honesty, Enfamil has been highly recommended to us by a few doctors as having the closest to breast milk nutrition. They have several different types, we personally use the Infant AR formula with Dr Brown's bottle line. You can sign up with them and they will send you a pack of coupons for $4 off a package.
http://www.enfamil.com Check this version out: http://www.viewpoints.com/Enfamil-Gentlease-Infant-Formula-reviews
On another note.. lets say the formula isn't the issue and your baby is just having a rough time and you want to help them out.. I massage my baby's belly to help her.. I also lay her on my chest with her on her back and I stretch out so she is arched.. It seems to really help her relieve herself. Here is some good resources that may help you help your baby :)
My Massage, I roll my fingers on her belly like I'm doing the wave on her lower abdomen, then I press down a little firmly when she starts pushing to help "squeeze" it out. I have stomach issues myself so I try thinking what I do when I am having issues and I apply same principle to her but in smaller scale.
I also mover her legs like she is riding a bike, or I put my hands on the bottom of her feet and let her push on them really hard. I stretch her legs out and push them back in and up so it kinda rolls her in a ball. In my head I invision that I am trying to "reform" the poop to a smaller or longer shape that will allow it to exit easier.
Helping her poop when she is having issues is one of my responsibilities and I think I do it pretty good :)
I can't answer your question specifically, but I would disregard any advice that tells you to choose a low-iron formula. I found a blog post that includes links to some studies. The idea is that iron supplementation is constipating, and it may be, but infants need iron to avoid anemia. Iron from supplements is not absorbed as well by the body as it is from whole foods, so excess unabsorbed iron is eliminated as waste. The baby needs that iron, however, so they need whatever their body can absorb.
My pediatrician has recommended a teaspoon of prune juice to a bottle when we've dealt with possible constipation.
Despite what manufacturers would have you believe, most/all formula is essentially the same. At least here in the US, all baby formula must meet a certain set of criteria involving the nutrients, vitamins, and minerals found in the formula.
Having said that, constipation is a very individual thing. Different babies will respond to different formulas differently, and you kind of won't know until you try them how your child will respond. If your child came home from the hospital supplemented with a certain type of formula and seems to be doing well on it, then I wouldn't mess with a good thing.
If, however, this formula seems to be causing the constipation then all you can do is start trying other formulas. There are certain brands that claim to further process their proteins which aids in digestion which might be a better option. Be aware, though, that this trial-and-error process is time consuming and expensive. You have to give your child a couple of weeks on a new formula to know if it's having the desired results or not. This means that you might buy several brands before you find one that's working and it might take a couple of months to straighten it out. In the mean time, the constipation might get worse before it gets better.
It might be better for you to find other ways of dealing with the constipation unless it's severe and/or you are absolutely certain it is the formula causing the constipation. It's important to remember that there is a difference between your child being constipated and your child just not having many bowel movements. Constipation occurs when your child's stool is hard and dense making them difficult and painful to pass. If your child is having normal, soft bowel movements, but they are infrequent then there isn't really anything wrong. Some kids only have BMs every couple of days. If you're sure your child is really constipated, then this website offers some good suggestions on how to help your infant including some diluted fruit juice, tummy massage, bicycle legs, and a warm bath. It might be good to have those options in your back pocket until you get the formula thing straightened out!