Oh, I hope your son loved his first day of school!
What birds come to your feeder depends on a number of things - principally (besides what birds are in your area to begin with) what type of food you put out and what sort of feeder you have. Of course, the big boys will go after the food if they can - they're hungry, too!
There are feeders designed to be accessible to smaller birds only. You might want to stop in a shop that specializes in bird feeding to see what's available - just to get an idea (some of these getups are pricey). There are bird feeders available in catalogues and online as well.
Different birds like different food. The Wal-mart mix may be a common blend with sunflower seeds in it, attracting a variety of birds, large and small. It's economical and easy to find, but we've gravitated toward feeding our birds millet (those little bitty white seeds that all birds like) and safflower seeds (which a lot of birds like but squirrels don't). We buy them in bulk at a feed store - it's perhaps a little more expensive than a discount store, but there is less waste because we aren't putting out any filler.
(We also have a large squirrel community in our neighborhood, and finally decided to feed the squirrels at the other end of the yard to give the birds a chance! We feed them ear corn, sunflower seeds, and apples.)
If your family really gets interested in this, you'll find many different kinds of feeders, because some birds like their food in hanging feeders, some on "trays," and some on the ground. We have put out suet balls and peanut butter in the winter for birds and squirrels both. Eventually you and your children will get to know what birds are what, and then you'll want a bird book and some binoculars. It can all become a whole lot of fun!
The advice to keep the bird seed outside is very good. It is packaged according to different standards than people food, and it can have bugs in it. If you store it in a close-covered metal container, perhaps in your garage, you'll do a little better on that head.