Southwest is a no frills airline. No meals are served and the aircraft (as far as I'm aware of) do not have tv/videos.
But what you will get for your hard earned money is an airline that has a high on-time percentage with few incidences of cancelled or delayed flights except for in the case of weather related problems.
You will also get a great customer service team that is usually very helpful, friendly and accomodating.
As far as boarding, you will need to go to their website for the particulars. The gist of how it works is that there is no assigned seating. When you check in you get a group letter. First ones checking in get A, followed by B, etc. And when they call for boarding, the A group boards first, followed by B...you get the picture. I have not flown since they started this system, so someone else can probably give you the specifics or you can access that info from their website. Also, check the airport SW counter early to see what they recommend is the optimal time to arrive prior to you flight... it can vary from city to city depending on the airport and the particular flight you're on. Some airports may request 1 to 2 hours. I know here in San Antonio, my boss frequently leaves the office at 9:30am to catch a 10:30 SW flight...the airport is about 20 minutes away and parking is easy.
There really is no huge advantage to getting a seat on the plane first - most seats are identical in legroom. However, since you have children, you'll want to check in early so that you can get seats together in a way that is convenient for you. Most aircraft, if not all, have 3 seats together on each side of aisle.
Having said that, if for some reason you are among the last to board the plane, don't stress. I've never witnessed where others didn't trade their spots so that parents could sit with their children. And if no one budges, then the flight attendants will gently coax other passengers to shift around for families.
If your flight is long, or you have a short interval between legs of your flight, I recommend that you take snacks/sack lunch and not waste time roaming the airport purchasing food. One of the biggest reasons SW is such a success story as far as airlines go is that they schedule their flights with little wiggle room at each stop. They can complete more flights in any given day (take in more revenue) by strictly adhering to this schedule.
If you're lucky you'll get a crew that is cheerful and interacts with the passengers...those are the most fun flights and they make you totally oblivious to the frills they lack.
Have fun!