The things in the basket change a bit, but are for the most part pretty standard. Some of the things are pre-individually packaged. Some of the things (like Goldfish) I put into my own little baggies. I just set up an assembly line of baggies, the snack, and a measuring cup and measure out an appropriate amount of the snack into each baggie.
The basket itself is a men's shoe bin from The Container Store. One of the organization blogs I read recommended them as the perfect storage bins for everything from snacks to toys. (I'm pretty sure this idea came from The Pretty Neat Company blog, but the blog seems to be down so I can't be sure.) And I have to say, I totally agree with her. I bought like 10 of them and they are now in use all around the house. They're just the right size, they're see-through so that you know what's inside even when it's up on a shelf, and they're sturdy enough to take some abuse.
The basket sits on a low shelf in the pantry. Low enough that every child can reach it. And now when I say, "Snack time!", the children can help themselves. No game of 20 questions.
This system makes me happy. Because it works so well for us.