Rules for TSA. Foods that cannot hold their shape without a container are liquids, and must fit in your 3-1-1 baggies (one 3-1-1 baggie per paid passenger, but you can carry all of them. Names on the bags make it easier through TSA with kids.). Condiment packets must be in your baggies if you have them.
Condiments already on food don't count as liquids. Your choices for ice are bags of frozen fruit, or empty baggies to be filled with ice once you get airside. SWA serves drinks gratis, and they carry juices if that is what you prefer for the kids. You can bring empty water bottles through TSA and fill them airside.
Best to avoid foods with strong odors such as tuna, etc., but as long as it is not liquid, anything they like will be fine. My kids thought Lunchables were a high treat on planes; they didn't normally get those. Packing snacks in individual small ziploc baggies will make it easier to manage mess. Bring some wet wipes.