We took dd to San Francisco when she was 10 months old via Newark with Continental.
I was HUGELY glad I'd booked an extra seat for her (it's not as pricey as an adult seat). We took her car seat and she slept a good portion of the way there and pretty much all the way back (night flight).
They wouldn't let us have a skycot for babies over 6 months, don't know if this really is FAA rules, but that's what they told us.
They certainly didn't offer us nappies, wipes, or to help look after dd! (or the person next to us who was on her own with baby twins...). Even more important for you to ask them if you have more than one seat is to seat you together! Believe it or not this woman with twins had 2 seats between the 3 of them and she had to fight to get them together!!! I'd recommend asking for the bulkhead, although not everyone likes it, as it gives the baby room to crawl at your feet.
We went summer 2002 so they were still rather post 9/11-y and hopefully things are better now. However, certainly no buggies on board. Neither were they available gateside - not until we had gone through immigration WHICH TOOK TWO HOURS! If you're a US citizen it should take less time but do be aware of this if you have a short connection time.
Finally, don't get too hung up on it all going perfectly! Go with the flow and it'll be fine...