You really do have to price everything out these days don't you ? It is just smart to know what you are willing to pay more for vs what is already "bundled" into a fare.
SWA and Jet Blue don't charge for the first checked bag I have also read that you can book AT via SWA and get the free checked bags but you have to wait for seat assignments until day of travel, FWIW I personatlly would not take that chance. We are a family of 3 and can usually do fine with 2 checked bags and one carry on with essentials for all of us for the first 24 hours.
When booking you have to look at checked bag fees and allowed weights, carry on bag fees, seat fees/early check in fees, and figure out what really is the best value for your travel $ and family makeup.
Sometimes a fare looks cheaper until you realize you have to pay for seat selection - sometimes that is as much as you would have paid for checked bags! IMHO you really do have to do your research and purchase based on the options that mean the most for your family.
I am helping my MIL book a trip right now and it has been interesting as her priorities are very different than mine. I find myself researching more and trying to make sure I get it right and make it as easy as I can for her.