I am finding that the post-snap read is the most critical. You can't read everyone post-snap - it's just not possible. Find a key or two on each play that will start to work you through your progresion.
If I'm looking at a fly route on the strong side against a 4-3, for example, my first post-snap read is the SS. If he's blitzing, I know I should be all good, and should just be seeing single man coverage on that reciever. maybe my second read on that play would be the MLB, to see if a slant dump off will be open across the middle.
But I would say, don't try to look for more than one or two reads on the defense. Think to yourself for each play : "If defender X does this ... I go to my WR ... if not, chek defender y. If he does this then, go to my TE ... if neither, but time or throw it away."
Setting yourself up with one or two key post-snap reads will do wonders for your game.
(Credit where credit is due: I am learning this now due to repeated a$$kickings from BK in NCAA.
)