I designed and built a great scrap bin a little while back. It's got a number of compartments which are perfect the types of scrap pieces have. I've been able to put everything into a good sized compartment, and put the whole thing on casters for easily moving everything around.

There are 2 types of compartment: top-access, and side-access. Top is generally good for smaller blocks and lengths, while the side access gives me a great place to stash longer cuts. On the back is a combination side and top access slot for full or large sheet materials. I think the design could be improved by adding some sort of removable cross-brace connection over the side-access of this compartment. I haven't loaded this up fully yet, but I'm worried about the amount of weight that back wall would realistically be able to hold.

It takes just slightly more than 3 full sheets of plywood to create, luckily, for the most part there's not too much wasted off-cuts, but even if there were. You'd have a perfect place to put them! Keep in mind that the saw kerf will make the 24" wide strips slightly less and plan your cut sequence accordingly.