For the most part, I'd suggest selling your items and buying better suited ones when you play a particular character. It's really kind of hard to determine if at the time you'd be able to use a particular bit of gear, if it would be appropriate to your build.
More often than not, if I stash a bit of gear I can't currently use on any of my characters, I end up coming back to it later and going "why did I save this? This is junk." Or I'll stash a halfway decent rare for a particular slot, and then get to the point I would use it, and I've found just one good piece of gear, and it's for that slot. (sigh)
If something has a very high primary stat for the item level, or if I find a legendary, sometimes I'll hang on to it. Most stuff, though, goes straight to the vendor. Interesting/exceptional rares end up at the auction house.
Instead of stashing random loot for twinking, I keep a few items on hand that I bought at the AH:
- A good socketed helm, for a +XP% Ruby (must be level 15 or higher)
- A good universal socketed weapon or two (several classes can use 1-handed swords, for instance) with a +DPS ruby
- Perhaps a couple of bits of +primary stat gear with low level requirements, just to make the early going faster.