ok i think I'm gonna throw in my two cents.
Instead of drywall screws, which work great with drywall, get some wood screws. I'll let you choose the size, but I think that it would be wise to stay away from 2.5" monstrosities. I assume that you know you need to predrill.
The wood screws that I am talking about have a part near the head of the screw without thread. Drywall screws have thread right up to the head. The non-threaded part means that once the screw goes through the first board and into the second the head is pulling the boards closer together, without threads holding them apart. Here's a link to a pic of the screw type I'm talking about. Hope your box goes well.
http://www.tool-net.co.uk/data/tools/28csposs.jpg