Thanks so much guys, I really appreciate your responses...definitely some food for thought - I've been really contemplating how difficult it may be to line up the dowels, even with a doweling jig.
From your perspective, as a relative newby to this, do you think the router route would be easier for me to take on?
Also, when you say dado corners, do you mean similar to the attached image?
Lastly, do dado corners offer as much / more reinforcement than dowels? Not sure if it is possible to say, just curious.
I've thought the "butt joint" corners would keep a clean look, especially if I am keeping the layers of the plywood showing in the finished piece.
As far as software, I used Adobe Illustrator to draw out my plans, I sit in front of a computer all day so I was able to devote a little time to the plans. I saw another user had used Google Sketchup to create some beautiful plans. Of course, I am probably setting myself up for a finished piece that looks nothing like the plans!
Personally, I think the router is much easier to learn and use and significantly more versatile than just about any other tool out there. It does take a little practice to get the right cuts though, so try some practice pieces first, if you go that route. (No pun intended.)
Dados are quite strong. Your image is actually an interlocking rabbet joint, also quite strong. Think of a dado as a channel cut out of one board, about 1/4-1/2 depth, that the other board just slides into.
In my previous post I was actually talking about the internal separators for the records, not the box sides, but you can do it for all of them. I would probably rabbet the sides so they don't interlock, for simplicity and ease of build as a newbie, but it's really not that much more difficult with the right bit set to do it like you've sketched.
Butt joints are the weakest joint out there so I'd recommend if you do that, you glue and screw them. If you rabbet/dado the joint you can probably get away with just gluing them but again, if you want sturdy, you can always overbuild.