Well since you have already have a Gold chocobo that means you have plenty of GP. Besides there are rare items for chocobo racing like Cat's Bell, Enemy Lure and Enemy away.

I suggest using Cloud cause well he should be your most powerful character now. He should have his ultimate weapon, a regen spell (Restore Materia) if your planning on all out attack, or carry a few other materias like enemy skills (Big guard works wonders), counter. I recomend getting the Curse Ring and equipping it on (to get rid of the timer you can connect the Added Effect+Destroy materia to negate the sudden death)