It'll take your baby a little while to reach 16 pounds unless you have a very big baby. Honestly, I'd concentrate more on size 2, which is 12-18 pounds.
Your baby's going to have around 8 diaper changes a day, and you'll be amazed how many diapers you go through. Hopefully you have friends and family who will give you some newborn and size 1 diapers (size 1 goes up to 14 pounds), so really I'd concentrate more on size 2. I personally didn't need size 3 for my daughter for a very long time, but she's a small baby.
It'll probably be a while before you need size 3. Months, probably. And during those months, your baby's going to be wearing either 1's or 2's.