Congrats! My little one just turned 1 on Saturday. Time really flies so enjoy it.
I have never paid more then 7 cents per diaper for newborn, size 1 and 2. And size 3-5 I have paid no more then 12 cents. I only have gotten the pampers and huggies since I can get them cheaper then the store brands. And onces in a great while the stores even pay me to buy diapers
CVS has been the place to go most of the time. They have great deals and you can use a cvs coupon and a manf. coupon together. Plus any extra bucks that you might have.
Target is also great. I always watch for deals to and they always seem to have a good clearance ever now and them(they even have some on clearance now.) And at Target you can also use a Target coupon and a manf. coupon. Plus if you have a Target card you get another 5% off.
And my last tip is buy a size larger if you find a great deal. My son is now in 4, but I have a good stock pile of 5 ready to go. Just so the math. It takes some work, but it is worth the savings.
Hope this helps!