I agree that the Dining Plan is a good deal, but only on three conditions:
1) You'd already be spending at least $38.50/adult/day (plus whatever the child's meal plan costs, can't remember right now)
OR
2) It's worth it to you to spend a little more money to get a lot more food
AND
3) Whatever you save on the dining plan won't cancel out a greater savings you might be able to get on a room discount
If you'd be paying rack rate for your resort anyway, then that last one's not a consideration. However, since you say you're looking for a way to spend as little as possible, I can tell you that it's definitely possible to eat at WDW for less than what the dining plan will cost you. You won't eat anywhere near as well or as much, but for lots of people, the dining plan gives you way too much food anyway.
My family did the dining plan last fall when it was free (which will probably never happen again), and while we enjoyed it very much, we didn't use it on our January trip because it would have cancelled out our AP room discount savings, and we knew we could get by just fine on about $30/person/day on food. We did this by eating most breakfasts in our room and having one counter service and one sit down meal per day, but not with a drink, appetizer, entree, and dessert for each person. Mostly we drink water at meals, and if we get appetizers or desserts we share them. We've found it easy to average $30 a day that way - some days may be a little more, but some days are less, so it all evens out.