When we moved into our house, there was a hand-made storage unit in the basement that I ended up commandeering for all my board games because of its near-perfect size.
The interior storage area of each shelf is 9 1/2" tall, 14" deep, and 48" wide. If you make the interior dimensions a little deeper and wider, you should be able to affix doors to the front.
The storage unit has no doors, so a few games hang out by a quarter- to half-inch, but otherwise, the dimensions are spot on, assuming you don't mind stacking games on top of each other.
Almost all of the games I have are no wider than 14", and 1" or 2" tall, which makes things nice and consistent.
To give you an idea of what it can hold, I'm able to fit the following games onto two shelves horizontally except where noted as being rotated 90 degrees with an asterisk:
Shelf 1: Carcassonne *, Puerto Rico, Risk, Axis & Allies, Dungeon, Hunt for Red October, Horus Heresy, two Munchkin games *, Boggle (Horus Heresy and Axis & Allies are stacked on top of each other with no more room; that should give you an idea as to how many "big-box" games you can stack on top of each other)
Shelf 2: Chaos in the Old World, Lord of the Rings, Mastermind, Power Grid, Buffy the Vampire Slayer, Scrabble, Monopoly, Upwords
Fireball Island and Battle Masters have to sit on top because they're too darn big.
Hope that helps!
