This is a pretty comprehensive list. YOU DO NOT NEED TO BUY ALL OF THE STUFF ON THE LIST. We'd eventually like the Scouts to accumulate and bring this stuff, but they don't need to right away.
They should come in their class A uniforms; when we get to camp we'll switch into T-shirts (troop class B preferred, but any OK). Real shoes, preferably hiking boots but sport-style shoes are OK. Sandals are OK for putting on for a late-night bathroom trip, but not as primary footwear.
There are really only four absolutely-must-bring items:
A $10 sleeping bag from Walmart is usually fine, though as the list says a stuff sack is much preferred over rolling-and-tying - the Scouts are just no good at rolling and tying sleeping bags. A stuff sack also helps to keep the bag clean and dry.
You should be able to put together a mess kit for less than $10, and might well be able to find what you need at home: sturdy plasticware is fine. Plate, bowl, cup, knife, fork, spoon (or spork is OK). (Pocket knife knife/fork/spoon combinations are undesirable because they are hard to clean.)
As for something to put stuff in, a duffel bag is probably the most likely choice... just so we don't have more than about two or three separate objects to pack per Scout. Typical is a duffel bag, sleeping bag, and pad.
If we're hiking, a water container is a requirement. It can be a Camelbak-style pack or a water bottle in some kind of carrier - shoulder strap, fanny pack, et cetera. A bottle that must be carried in your hands is not acceptable. Start at one liter for modest hikes; two liters is better.
The next tier is probably a pad, either foam or inflatable. My children like the Therm-a-Rest Z-lite, about $40 from REI. (Probably less elsewhere.)
Spare clothes are good. We don't usually expect to get wet/dirty, so they're somewhat optional. If we are expecting to get wet, more is good. Remember, though: this is camping. It's OK to come back stinky. (If this was backpacking, coming back not-stinky means you packed way too much.)
Sunscreen. I hate sunscreen more than I hate sunburn, but I hate skin cancer more than I hate sunscreen. 'nuf said.
Hats. See sunscreen. Some people like baseball caps; I don't - I want my neck covered. Crushable is in my mind a requirement.
Soap. We wash hands before every meal. If it's a bar, put it into a container. A baggie will work.
A flashlight and spare batteries.