First, you'll need at least 100,000 gil. This may seem like a lot to you,
depending on when you decide to start breeding. But, each stable costs
10,000 gil, plus you'll want 25,000 to buy some Sylkis Greens for upgrading
and some Gizzard Greens (or Gys-something) to catch Chocobos. Talk to the
Chocobo Sage (Near Icicle Inn and south of Crater) to buy Sylkis Greens.
Once you have at least 3 Sylkis Greens and some Gizzard Greens, catch a
male and female Good Chocobo (refer to key at bottom) at the tracks west
of North Corel. Once you've done that, catch a male and female Great
(once again, refer to key) Chocobo at the tracks in the Mideel area. Give
a Sylkis Green to each of them and get them to B-Class if possible. Now,
you'll want to find some Carob Nuts. You can get them from the large red
dragon-type monsters in the Bone Village area with the Steal [Command]
Materia. Go back to the ranch, breed the male Great and the female Good
together. You should get a blue-tinted Chocobo (or green-tinted, I forgot).
Anyways, breed the female Great and the male Good together. You should get
the opposite color of the other pair. If not, reset and try again.
Once you have a blue-tinted and a green-tinted Chocobo, buy some more Sylkis Greens (around 16 total, which is 80,000 gil), and give eight to each of the new Chocobos. Get them to A-Class, S-Class if possible. Now, breed them together with a Carob Nut. If you don't get a black-tinted Chocobo (which is mountain- and river-crossing), reset and try again. You will now need to catch a Wonderful Chocobo (I shouldn't have to tell you to look at the key) at the tracks near Icicle Inn. Make sure it is the opposite sex of your black-tinted Chocobo. Oh yeah, you'll need another 8 or so Sylkis Greens (each) for the black-tinted Chocobo and the new Wonder- ful Chocobo. Feed them the Greens, and maybe some Gizzard Greens for stamina and some Krakka Greens for intelligence. Now, send them to the Chocobo Races and get at least one of them to S-Class, if not both. This increases your chances of getting a champion Chocobo of the correct color. Once they are ready to mate, go to Goblin Forest on the east side of the world. Steal at least 2 Zeio Nuts from the Goblins you encounter there and mate the black-tinted and Wonderful Chocobos together. Pray for it and you should get the ultimate Chocobo...the Gold. It can cross oceans, rivers, mountains, practically anything. With this you can get infinite Counter Attack [Independent] Materia, infinite Turbo Ethers, and thousands of GP at the Chocobo Races, not to mention the Knights of the Round [Summon] Materia, the Mime [Command] Materia, the HP<-->MP [Independent] Materia, and other stuff from the Materia Caves scattered about the world.
So, you want to know what all this S-Class stuff is about, right?
Well, once you have your own Chocobo, you can race it in the Gold Saucer for
prizes or GP.
The only Greens you need to know about are Sylkis (5,000 gil each at the
Chocobo Sage's house), Gysahl (100 gil each at the ranch), and Krakka (500?
gil each at the ranch). Sylkis will cover most of your needs, but if you
need to bump up stamina, use Gysahl. The same goes for intelligence with
Krakka.
