Before you head to the Gold Saucer to start racing make sure you have all of the Chocobos that will be needed to mate and make sure they are the correct genders. I would also suggest making sure that you have all of the nuts needed as well before hand, just to make things go faster once you are ready to mate.

Another suggestion is to only use Sylkis greens. This is because they will increase your Chocobo's attributes the most. However they are expensive, but I know a little trick. If you find a W-Item materia you can use that to duplicate items when in battle. All you need to do is select the Sylkis greens as the first item and then select a second item. After selecting the second item cancel the command and this will copy the first item selected.

Another tip, for racing this time, if you feel no moral objection to cheating the races, hold down the R1/2 and L1/2 buttons at the same time you can replenish your Chocobo's stamina.

One last tip, ALWAYS SAVE before mating. If you do not have the outcome you were expecting you can reload the save file and try again with out having to repeate the process of finding new Chocobos and racing them.