I would freeze as much of the food as you reasonably can. It will help keep things as cold as possible without using so much ice. There are a couple ways to go here but only you know what will work best for you.
I like to precook my food as much as possible, then pkg them in proper sized bags for a meal of 2, 4, or what ever.
I like to have a separate cooler just for drinks & common use items, that way, your food cooler stays colder longer & with less ice.
There is also the "dry ice" option. Use gloves with this stuff & don't let kids touch it with bare skin.
Finally, there is the cooler itself. Personally, I could NOT bring myself to spend $500-$600 on the latest, greatest cooler. For not much more $$$, you can have an ARB 50 qt fridge/freezer & never, ever have to worry about ice again. Yes, these things work & work excellent. There is a LOT of truth to the statement: "once you get one, you'll wonder how you ever got along without one."
We bought an 82 qt & a 50 qt. The 82 has been plugged in since the day we got it. Last summer, it was 85* out & before we went to bed, I took all of our freeze bottles for the drink cooler & put them in it at 11:00 pm at night. At 7:30 am, it was reading -1* F & bottles were all refroze solid. (We just use old cool-aid containers filled about 3/4 full w/water & rotate them everyday) for our drink cooler. SO NICE not to deal with getting ice before the stores close or sells out.
Some coolers have no insulation in the lid at all. I feel they lose most of the ice this way. Older coolers are just double walls as well---with no insulation in between. You can make a cheap cooler work a LOT better by insulating the walls & the lid with great-stuff. But be aware---there are like 10 different kinds now. You would want this:
http://greatstuff.dow.com/product/window-and-door.htm . The other stuff expands too much & may make your lid & walls move enough so it won't close anymore & you don't want that.
Then there is Capt. Obvious: don't leave it in the sun, fold up a blanket & put it on the lid to help keep cold in & heat out, don't leave in a hot car, etc, etc.