If you are on a budget, I would say to stay at Pop Century and get the dining plan. With the regular dining plan, you get 1 table service meal per person, 1 quick service meal per person and 1 snack per person for each night of your stay. Plus you get one refillable mug per person to use at your resort. Each quick service meal comes with a beverage and a dessert. Since you would already have your refillable mugs, try to eat your QS meals at the resort so that you can use them. Get juice or milk for your included beverage and take it back to your room. Place it in the fridge for breakfast the next morning. This will cut down on out of pocket expenses for breakfast! Trust me, it adds up! The breakfast platters are a pretty good size and can easily be split between 2 people if you aren't huge morning eaters. Since the dining plan only gives you two meals per day each, you will need to pay out of pocket for the third meal...breakfast is always the cheapest even when you are going to a character buffet. (they serve food....not characters!)
You can bring water into the parks, so I would buy a few cases of water to keep in your room. Bring a few bottles into the parks and fill them up at the fountains to save money. You can always grab up a few crystal light packs or tea packs to add a little flavor!
Buy your spritzer fans at your local dollar store instead of waiting to get them at the parks. You'll pay three times as much if you wait! The same goes for rain ponchos!
If you decide to pay out of pocket for all of your food instead of getting the dining plan ahead of time, I would still grab those refillable mugs. In the long run you will still save money. Quite a few of the quick service meals around the parks are big enough to share...at AK go to Flame Tree BBQ and get the chicken and ribs platter. Plenty to split!! For the kids, you could always order a double cheeseburger wherever you end up and ask for an extra bun (not sure if they are charging for that now...you may want to ask). Also, alot of your meals come with a side salad. If you don't really want it, ask them to leave it off. Should be a difference of a few dollars! If you are at downtown disney, go to Earl of Sandwich for a quick bite. They have really good sandwiches and it won't break the bank!
All in all, have a good time and don't sweat the small stuff!