If you really want to get the most out of the game, then beat Sin/final bosses first. Otherwise, it is a waste of time to explain the method to you. It's not hard, just long, requires perseverence, and you may end up resetting. Alot. And I mean... alot.

And yes, since the cave at the bottom of the gorge is filled with monsters you cannot yet beat, I would save it until you are at least past Zanarkand. There are no items that you miss that cannot be obtained in large quantities later in the game. Except the Al Bhed primer also in Bevelle, but if you missed it, just start a new game, and compile the primers once you have them all.