When you build your drawers I'd reccomend that you make them shallower than the DVDs and tapes on the sides so you'll be able to grip them at the edges. The drawer fronts will of course remain the same. Also, put spacers of at least 1/2 inch between rows of DVDs. The temptation to get them really tight is always there, but your frustration in trying to access them will be high. If you orient the DVDs so you can read what they are from above you'll be happier. I make my drawers with dados every inch or so to be able to drop in dividers wherever I like.
Good luck!
Good luck!