It's better to count the cards as they are being dealt, for two main reasons. One is that you'll want the most information you can get for playing decisions, and especially insurance decisions. The other is that if the dealer has a blackjack, and you're counting the cards as each player plays his hand, you might have a lot of cards to count in a very short time.
And yes, you've got to be quick, but there is just enough time to get it done, even if you're playing first base.
Side note: I've been playing for almost four years now, and it was just 3 or 4 months ago that I finally switched to counting the cards in the right order.