Book your meals. Then when you have them fairly set, add up the cost and compare that to the cost of the dining plan. If it works out about the same or less and you feel the plan will make things less stressful, (this seems to be the biggest argument for doing it), call and add the plan.
Most of the time the dining plan offers no great discount or real price difference between the plan verses paying out of pocket. Every now and then, Disney will offer
free dining or discount packages. Keep an eye out for these, then do the math on if it would be worth it to switch to one. It really depends on where and how often you plan on eating.
This is what we always do. We have always come out better not doing the plan, even when free dining was offered as we would have had to pay rack rate for the room which we got a massive discount on worth much more than the cost of our meals each day.
We will be using the plan for the first time ever next trip. I couldn't believe it when I did the math and came out about $300 cheaper, not even counting the cost of the snack credits or the refillable mug as we don't normally do either. This is a first for us. I was able to book a discounted package. I then priced out
UT tickets, a discounted room only rate, and the cost of the meals I knew we were planning on doing each day. That price came out $300 more expensive than the package which included the dining plan.
However, I'm not quite sure how I feel about the plan. On the one hand, it will be nice to pick restaurants solely based on if I want to eat there without worrying about cost, but on the other, I do worry about restrictions and keeping credits straight which seems more stressful to me than simply ordering whatever I want and handing over my credit card.
A few other things to keep in mind:
Everyone in the room has to be on the plan. With your children's ages, many people paying out of pocket might opt to have them split meals with others in the group. There might not even be a need to purchase meals for each child except at buffets, so the dining plan might work against you in that regard.
Secondly, for first trips, especially with younger children, many people recommend booking only a few table service meals. Definitely not the 1 meal a day the dining plan gives you. To me, the dining plan seems to work better for those willing to focus more on meal experiences than attraction experiences. Meals can take up huge chunks of time. For a first trip where there's so much to see and do, you really don't want to be eating up that much time each day with meals, unless sit down meals are your favorite thing. TS meals can last anywhere from an hour to 4 hours. I estimate 1.5 hrs in my planning, and I'm not counting the travel time to and from the restaurant in there. We once waited 2 hours to be seated at 50s Prime Time and then the meal took 2 hours! Not the norm, but it does happen. Then factor in that going to DS to eat, takes even more time, as there is no quick easy way to get there and back. A visit to DS, usually involves a 3 step transportation process which can take a few hours by itself. Again, do you really want to loose 4 or more hours just on a meal? Definitely keep in mind travel time and realistic meal durations when planning your sit down meals. Don't think you'll be in one park and just hop next door to eat at a different one a few minutes later.
Third
Check the menus for the TS restaurants. We've had issues with picky eaters and even my not so picky eater finding things to eat on the TS menus. Which I don't blame them as there isn't a lot on many of the menus I care to eat either. When the kids were younger, this greatly reduced the number of places we had available for us to eat at. I'm not sure I could have come up with one TS meal a day back then.