One more thing. They will need an official state-issued Birth Certificate in any case. Not just a Hospital one, one from the state they were born in.
So if you aren't sure if you have the right thing, double check.
We decided to get passports for our boys and the week before our appointment at the post office I went to the file cabinet drawer where I had (I thought) placed there birth certificates 14 and 15 years earlier, only to find that one of them was missing. It took 4 weeks for the state of to send me a new one. (The state DS was born in, not the state we now live in.) So I had to reschedule our passport appointment. Luckily we still had plenty of time, but for us, getting passports had the advantage of making sure we had their proper birth certificates. This will come in handy again in a couple years when they go to get driver's licenses. (Yikes!)