Drawers are probably not going to work. First of all because they are usually the wrong dimensions, and secondly because they are probably not designed for that much weight. (I had a couple of dresser drawers full of them, and the drawers would *not* stay shut.)

What I settled on is abusing a kitchen cabinet with movable shelves of size 22x24. I put 2 boxes on each shelf of dimensions 10.5x21.5x3.25, each of which holds 30 inches of standard paperbacks. (Yeah, 3 boxes across would hold slightly more, but meant a lot more boxes.) Add some extra shelves and you get a lot of books into a free-standing unit.

Cheers,
Ben