You can go to your airports website to see what airlines go in and out of your city. Southwest is great out of Dallas, but if you are in Houston I think that is Continentals hub? So if you want a non-stop you are more likely to get one with an airline that hubs in your city OR in the city you rae flying to.
Get to the airpost at least an hour and a half ahead since you are a first time flyer.
If you want to carry on liquids and gels must be in a ziploc bag…one bag per person and the liquids must be in containers less than or egual to 3oz. So, you can fit 3 or 4 in a large sandwich bag, and that is about it. This includes liquid make-up, suntan lotion, etc. If that won’t work you can just put it all in a checked bag.
Security will most likely have you take off your shoes, so if you HATE the idea of having barefeet on the floor, wear socks. Some airports have paper slippers but not all of them.
Once you board the plane buckle your seat belt and keep the seat in an upright position, and the window shade must be kept open.
Once everyone is seated they will pull back from the gate, travel to the queue to take off, sometimes you can be lined up for a long time. Once the plane pulls back from the gate you will not be aloud to use the bathroom, so make sure everyone has gone to the bathroom. Literally if one of your kids is desperate they will NOT let her/him get up.
Once you are in the air flight attendents will prepare to serve drinks and they sell some snacks. You can bring your own food and drink on board, although drinks must be bought gateside of security (because remember you can only get that ziploc bag through with liquids). Eventually, once you reach cruising altitude they will let you get up from your seat. You can close your window shade if you want to block the sun and rest, and you can recline your seat. About 20 minutes before landing they will put on the seat belt sign again and again you cannot get up, so if you or anyone else has to “go,” try to go before the sign pops on. Typically they actually will let you go right as the sign goes on, unless there is turbulence, but there is more likely to be unpredictable turbulence while decending. You will be expected to prepare for landing, which means all seats upright, all window shades up, and all seat belts buckled.
None of that is to scare you, I fly all of the time no mishaps, rarely any turbulence. Just so you can anticipate things.