First of all, the best place to get the highest quality chocobos is in the snow-covered area in the north (the tracks are on the western part of that island), but remember this: the chocobos will only be good if they appear with just one or two of those bouncing rabbits (their exact name escapes me).

Second, breeding certain special chocobos can only be done with a special type of nut that must be stolen from the Goblin enemy (they appear on those narrow islands on the northeastern part of the map).

As for what greens to use, that shouldn't be too tough to figure out, but ask the Chocobo Sage if you need more details. If that doesn't help, then I'm sure there's at least one FAQ dedicated to chocobo raising on gamefaqs.com. Just remember to be patient, and be prepared to burn through thousands upon thousands of gil to get the chocobos you need.