Sorry in advance; this post is a little rambling and disorganized, especially compared to the fine OP.
I keep old missiles in stock. I tend to buy them whenever I refresh the shop, and I prefer not to throw away useful things, so I have a ton of them in storage waiting to be slowly used up.
I have four sets of gear for maximizing stats for skill missions, so that's 2 storage tabs.
I like to save clothes for possibly making themed movies, so I frequently save headwear, chestpieces, legwear, and belts. The quick pace of items growing old obviously means that there is a lot of stuff being sold, especially items gained from duels (unless they improve on my stat-specific skill mission items). I usually only save epic items though, since I hate to pay diamonds to use the sewing machine in case I want to get my hands on a specific item for a movie cover.
The only item I wear that has to be epic is the chestpiece (yeah, I feel like a child these days when I put on common skill mission gear and revert to standard boobs rather than epic boobs) but other than that I have no preference of item type as long as the stats are better. For some reason I really hate the blood bags and some of the legwear, so if I want to use them as part of my main outfit (the clothes I wear when not dressed up for skill missions or for a movie cover) I'll sew them into a neat common item (I'm cheap that way, and there are some common pants that I really like anyway).
I try to use the washing machine for the achievement rather than out of a desire to change the stats of an item, since I (rightly or wrongly) have become convinced that maximizing a single stat is very inefficient and that you should strive to keep all stats high or else you can still get your butt handed to you in the long run and a few hundred SP up or down between two stats don't seem to matter all that much.
Free refinements are excellent, though occasionally I pay for them when I get too frustrated by bad draws.