I base most my info from a GameFAQs guide
I will assume that you don't care about the difference between a 4th strategy and 1st strategy Chocobo. The following is true for a 4th build, but either a Gold or Silver will do the same with a 1st strategy, since they both have to waste a slot (+40% magic or Blue Streak).
From your comment you are looking for the best possible racer, that is going to be the Silver Chocobo. Chocobos are ideally fed only Potent materials, and a Silver Chocobo will get an A rating in both Speed and Endurance (based off of Strength and Magic) a Gold Chocobo will end up with A/B. This will require infusing a +% magic, such as +40% magic from a Tonberry.
Once you have capped it, you will need to infuse abilities into it. I don't believe it is possible to get every possible ability, so focusing on the Chocobo's natural strength is best. In the case of the Silver Chocobo, it gets Blue Streak naturally, so focusing on the 4th strategy will result in the "best". Given that, the ideal build (and the passives that make it up) would be:
- Blue Streak (Ally KO: Power Surge)
- Second Wind (Improved Counter)
- Sprinter (Critical: Bravery)
- Marathoner (Critical: Vigilance or Tetradefense)
- Limelight (Kill: ATB Charge or Libra)
- Dark Horse (Item Scavenger II or Item Collector)
- Attention Hog (Feral Speed II or Gilfinder II)
- Rocket Blast (Any 3 resists, Role Resonance, Feral Surge: Fatigue)
I built my own Chocobo like this, to improve the odds when using Chocoboosts, but Health Nut can be added if you don't want to spend the coins. Also, I don't think I was ever not the favorite, so it was a moot point anyway.
I don't have experience with Free Spirit, so can't comment on it, but you can get a Microchu to 35 to get it. And if you want to skip Health Nut, you can use a Microchu at 18.
With all that out of the way, here is a set of things to infuse to get the above abilities, order doesn't matter since we only have 7 to infuse.
- Pulse Gladiator 1 (Second Wind)
- Cactuar 1 (Sprinter)
- Microchu 24 (Marathoner, Dark Horse, Health Nut)
- Goblin Chief 22 (Limelight)
- Moblin 1 (Attention Hog)
- Frag Leech 30 (Rocket Blast)
Make sure the ability counts line up (one passive per ability) before committing. More info can be found in the guide I linked.