What is a good strategy for selecting commons and uncommons for trade folders?
There are really three distinct things you're looking for:


Playability in Standard
Playability in Vintage/Legacy
Playability in EDH/Commander and other popular variants


The first two are actually fairly easy to gauge; the more playable a card is, the higher its price is (typically).  Use something like Magic.TCGPlayer, http://magiccards.info/, or another pricing site to look up your cards and see if they're of value.  Alternatively, you could look up lists for the most playable (read: highest value) common/uncommon cards in those formats and look for those cards specifically.

The third option is a little more difficult; since EDH decks are built with 100 cards with no more than 1 of any given card (besides basic lands), lots of commons and uncommons are more popular and playable than in Vintage/Legacy.  I'd recommend looking up lists of common and uncommon EDH staples and seeing what cards you might have.

The key thing you're looking for really in any card is the effect-to-mana-cost ratio.  Cards like Swords to Plowshares, Lightning Bolt, Mana Leak, Terminate, Sensei's Divining Top - things that are cheap with powerful effects are really what see play.