I do clothes in the first section, furniture in the second, and everything else in the third.
Once I unlock more rooms in my house, I'll start using the second section for clothes, too.
I've got rare fish and sea creatures in Drawer A; rare bugs in Drawer B; and hybrid flowers in Drawer C. my other rare items i've stashed in an alt's closet in no particular order.
I have no idea why I need to have my own personal specimen of each rare fish and bug, but I can't let it go, I just dooooooo.....
How do you have the space though? I've just moved a bunch of things over to my alt because I had no space in my mayor's closet anymore and I'm so glad I did. But I would never have space if I kept fish and bugs in there! I do have some bugs and fish on display though (a cricket, a sea butterfly and a goldfish).