Hi Jin, it sounds like everyone has given you great advice - I travel a lot for work and with my daughter (who is now 3) so thought I'd pitch in as well.
First, snacks and drinks: If you are able to take liquid through security (which I doubt but have never tried), I would guess it would be more of a hassle than just buying after you get through security. Always buy at least one bottle of water after going through security - one for you too, as it also can help with the ears and it helps prevent sickness as well. I've been known to get both juice and water and mix it up so that my daughter will drink enough without getting too much sugar (she never notices unless she catches me doing it! :)). Also be sure to take either zip lock bags or some kind of reclosable container for snacks - I usually mix up a few favorite snacks so we don't spend all the time negotiating which ones to open.
Second, if you are taking diaper cream or anything like that, you will want to put it in a zip lock bag (a quart or less) because they sometimes consider this liquid. AND you'll need to take it out of any other bags and put it in a container directly. They'll let you get away with more than 3 oz for diaper cream (or at least I have), but they definitely like it if you put it in the bag first. Don't forget the 3-1-1 rule for everything else (3 oz in one bag that is one quart or less - can you tell I've heard that too many times!?) I have gotten caught on more than one occasion where I've left lip gloss or something in a side pocket and they have to search my bag. This includes ANY liquids or liquid-type things, even toothpaste.
Last but not least, if you are taking a stroller, you will need to empty it and fold it up to put it through the security cams (along with jackets, shoes, etc... ), so try to have everything already in a bag with your camera or camcorder on top so that if you need to take those out, it's an easy grab.
Sorry for the length but I wanted to cover everything!! Good luck!