Breeding Chocobos is avery good idea. You can get money and prizes on Gold Sauser, and you cant get Knights of  Round with out a Gold Chocobo. Heres the way to get one.

First, get a "Good Chocobo and  "Very Good" Chocobo. Let them mate, and give thm a Carob Nut. You get Carob Nuts from a big red dinosaur in the grassy areas in the Snow Fields. When they have breaded, you should have a water chocobo or a mountain chocbo, depending of wich sex the "Good" chocobo was. If the "Good" is male, you will probably get a mountain.

When you have gotten this far, you should try to get a male mountain and a female water chocobo. When you have, mate them with a Carob Nut. If they get a Black Chocobo, you have got the right thing. The Black chocobo can go both on Shallowed Water and in Mountains. Now, you should catch a "Wonderfull Chocobo" to mate with the Black Chocobo. Give them the nut that you get from Goblins on Goblin Island. When they have mated you should have a Gold Chocobo. The Gold Chocobo can go everywere.

Note that it is easier to get the chocobo you want if the parents are in a pretty high class. To get them in a better class, you should run with them on Chocobo Square. If you manages to beat Joe (you remember Joe, huh?) the right amount of times, you will reccive all the prizes that you can get from winning.
 

If you have a chocobo in C class, and it runs in about 110 km/h, you should ride it a while. "Why?", you think, "why dont I ruide it allway if its that good?" That ios because it probably is a chocobo that wont be leveld up. So when it comes to S class, it will be a very slow runner. It will even be hard to win with it in the A class.

Feed your chocobo often. This will make him/her be beter. Try various greens untill you find the one that fits good for your chocobo. What you want to raise most is Speed, Intelligence and Stamina.