I'll generally try to look at each child's adoption screen at least twice before deciding, based mainly on their money-making potential and preferences for kids. In my last game I looked through each screen of the six kids about five times. It was so difficult to choose between them that I ended up picking one of them almost at random.

well, I choose the one who really looks like my very first character . :P so that the genes will stick up to the very last generation. :P

Savannah, when you choose to go to the second generation, all children automatically become "of age," even those who were still at home.

I choose based on salary and amount of money the family has on hand. My second factor is whether or not they "definitely" want kids, because if so, I know I have to take the first proposal or find some other way to keep them happy fast.

Edit: I should specify that by salary I definitely do not mean that I choose the highest starting salary. I go by the information we have collected on salaries in this thread

I generally go based on salary and looks. I rule out the ones i didnt like anyway, and out of the ones left, i usually pick the one with the highest salary. I dont go by their preferences on kids because it doesnt seem to ever make any difference. For my first family with 6 kids, the dad thought it would be nice to have kids and the mom said not really.

If there was a kid whom I particularly liked growing up, I will choose him/her. (One of my first washed the dishes within minutes of mommy letting him run free. He was a very hard little worker, and cute to boot.)

If none of them have won my heart, I go with the cutest. If none of them are cute, I move on to money and willingness to have kids.

I kept the first one ¬¬
Didn't know that i could choose
Noobie me

Personally, I go by desire for children and salary in the early generations. Later on I trend towards looks and careers.
Other times I just develop an attachment to one of the kids for one reason or another while they're growing up and choose them.

I(with my farthest generation being number four) generally pick by if they want kids, theyre age, and they're salary

I roll a die and determine mine randomly. It makes it kind of fun the suspense of not knowing and hoping one of my favorites will make it.

That's what I do, too, although I tend to carry it through all the generations, not just the early ones. That's not to say that if a particular peep has caught my fancy, I won't pick him or her, though.