Are you planning to anchor it to the wall? A swinging cabinet that large is going to pull the stationary part of the cabinet over, possibly even when completely empty.
I'm planning on building a cabinet for my DVDs soon, and I have decided to make the front shelves split in the middle, so each is 1/2 the width of the back stationary cabinet and hinged off both sides of the stationary cabinet with piano hinges, but I'm still thinking that I should attach it to the wall.
I'm also planning to make the base and the top of the cabinet the full cabinet depth of the closed cabinet, so the front swinging cabinets will be more like doors off the rear cabinet. The base will be heavily reinforced too. This should help significantly with stability when the front cabinets are hinged open. I was planning to install locks top and bottom in the stationary base and top to keep the swinging cabinets closed, but I may not install locks at all, and just depend on magnetic catches to hold them shut. I don't really need to lock mine. I'll also be drilling the hinges so that I can add 2X the number of screws, and will use longer screws than those included with the piano hinges.
A small lip of about 3/8" on the front edge of each shelf, rather than sloped shelves,
will keep the DVD boxes in place and will be easier to do, but it will only be needed on the moving shelves. Just make certain that you space the shelves vertically so there is a 3/4 - 1" gap above the DVD boxes to allow them to be lifted as they are pulled out. DVD boxes are not as deep front to back as most books, so you will need to decide on the depth that is really needed and consider leaving the lip off of shelves that will hold books.
Central North Carolina