You're going to get 100 different people respond, with 100 different answers as far as the perfect level of storage. It all comes down to how your family packs, and what's in your room. We (family of 4, one being 4 months old) did a 4A so we had extra room for the pack 'n play. We also got a double steamer trunk, which we wouldn't have been able to live without. We took an over the door shoe organizer, and used it to its fullest potential!

We had enough room with all that. A closet organizer like you're talking about would have been good for us, as we had the steamer trunk jammed packed but didn't have as much hanging stuff. I'll probably pick one up for our next cruise. I also liked the idea mentioned above for two over-the-door shoe organizers, and I'm really surprised I didn't think of that...
We are mid-heavy packers. We don't do laundry while we're travelling, and we pack a few extras of everything just in case. We had to with a baby who you never knew when the spit-up was coming...

We'll usually end a cruise with a few items still clean and unused.
The door organizers are completely personal preference. We'd never go without them, but others will tell you they aren't needed at all. There are ample shelves in the bathroom(s), at least I think so. But in our case, DW has so much specific stuff for everyone... DW, DD, DS all have a separate bottle of lotion (DW has more than one), kids have two separate sunscreens from us (body and face). DW and DD each take an unfathomable number of flip-flops, dress shoes, etc. Hair dryers... brushes... makeup kits... Our counter tops would be over-crowded if we didn't have the shoe organizers. I don't ask about the excess... I just pack it all into suitcases.

I personally have one small toiletry bag for all my stuff.
Here are the best things you can do/know for your situation:
1) Cruise once, experience is the best indicator of what you need
2) Check out:
http://disneycruiselineblog.com/ships/disney-magic-wonder-steamer-trunk-stateroom-list/
See if your room has a double, single, or no steamer trunk. The double we had was quite large!
3) If at all possible, use collapsible duffel suitcases instead of the big framed ones. My favorite suitcase we have is this one:
http://www.costco.com/fūl-2-Piece-Wheeled-Duffel-Set:-28"-%26-20".product.11760945.html
It's light, packs and amazing amount of stuff with separate compartments, and folds down.
The reason I say this is because every other cruise ship I've ever been on you could store your suitcases under the beds. On the magic, our three big rectangular suitcases (pretty traditional) wouldn't fit under the beds. We had to put two of them between the bed and wall on my side of the bed, and the other one against the wall next to the TV. That was more annoying than anything else.
Sorry for the long post, hope it helped