Solid woods vs Plywood for box joints
The best way to create box joints for drawers I believe is the old method of finger joints. You can make them either using your router or buying the right type blade for a table saw.
Now I tend to agree with BJ on plywood is basicaly good for bottoms, and the use of solid woods for face, sides and back, but if your gonna use plywood all around the finger joints are the method of choice.
However I would use cabinet grade plywood rather then say Arrouca Pine, or other standard sanded pine.
Now hardwoods allow you a much more solid joint and edge grain look to your drawers, Oak, Birch, Maple, and Poplar are great to work with and stain real nice as well, draw back is its usualy sold by the foot and not like select pine sold by the whole length of piece.
Hint: I never shoped at Lowes so I do not know if they do the same. I work at Home Depot in the lumber dept, we always carry what is known as "Cull lumber" usually peices cut to 3' to 5' lengths and sold for as low as $0.51 cents a peice, its a nice way to get wood cheap!