The advice given so far is sound.
I highly recommend no more than one meal per day in the parks. You can even get away without that if you are in a nearby hotel and can just walk back for a break from the action and have a nice meal back in your room. Telling the kids to wait until the last day to buy their souvenier is an excellent idea too and having your meal outside the park can help you afford a little more on that last day.
Yes, water bottles are a bit heavy but the good news is, the pack gets a little lighter as the day wears on. We freeze water bottles (don't know if that will be an option for you). If you can pick up some reusuable water bottles with straps that would be even better. Everyone carries their own. There are quite a few Disney themed items out there. We picked up a few in the
Disney Store just the other day for $6 each. Water bottle, carrier and strap included. That was on sale so not sure if you can still get that deal, but others are out there.
Absolutely carry plenty of snacks and even the fruit that was suggested. One thing, bring napkins and ziplock baggies. Also, get a variety. Everyone will get tired of the same granola bars after a couple of days.
If you have it in the budget to eat one meal in the park, I've found Red Rockets Pizza Port to be a decent value. You get plenty of carbs which are both filling and give you energy and the portion sizes are pretty good for the money. You can even get a decent salad if you prefer. I try to stay away from the burger/fries. Also, try the Big Thunder Ranch BBQ. It is on the expensive side but it is all you can eat. So, if you're only going to do one meal, why not do one that you KNOW you will be good and full when you leave. There is also a decent value and variety at the Mexican restaurant over near the entrance to Big Thunder (can't remember the name right now). They have a variety of choices.
Check out all the menus, as was suggested, to determine exactly where you want to spend your food dollars. Bottom line, you can have an excellent time without spending a fortune. Just lay out your budget and then don't worry about it.