If all you want to focus is physical stats (which is what you should be focusing on for winning those races) then feed to adult chocobos: 2x Sharug, 2x Vomp carrots (in this order).
Use "Carry Packages" as plan, and use "Take a walk" plus if you want "race with others" and lots and lots and lots of Watch over chocobo.
Make always sure your chocobo is always as max affection (message should say it regards you as a parent). If you don't get this message you're gonna get a reduced amount of points from plans and interactions alike.
After day 43 if you're satisfied with your physical stats (i.e. if they're at "outstanding" or "first-class" level) you can start to focus on mental stats, feed Zegham x2, Azouph x1 (in this order), change your plans to exibit to others and use "Tell a story" as interaction (and lots of watch over!)
If you wonder "why should I bother about mental stats?" they are kinda necessary for your Chocobo to learn abilities. For a racing chocobo you mostly want Canter (greatly increases your endurance) and Gallop (greatly increases your speed). Think of them like passive traits for your choco, not real abilities.
Keep in mind these are totally not necessary to win up to the CRA classic race.
Also, as far as I know feeding and doing "physical" stuff, doesn't affect mental stats, and the other way around.
This is not true for "care plans". A physical-alligned care plan is gonna lower your mental stats and vice-versa.
This kinda mean that from when you start focusing on mental stats (don't do it before day 43) you're going to slowly lower your physical stats, which is why I told you don't bother unless your choco is either at "Outstanding" or "First class" in them.
Once you've learned either Canter or Gallop you can spend the rest of your days focusing on physical stats once again, trying to get as high as possible.
To win the races up to CRA you "need" outstanding in both endurance and strenght.
Well this is actually not true, you can probably do it with "impressive" in both if you use speed apple, but the problem is that these ranks are very generic.
For instance "Impressive" goes from ~160 points to ~191. If you get exactely 160 in both that might be not enough, but 180 will probably be more than enough to win all races, with apples and a bit of luck.
That is to say that "Impressive" alone doesn't mean a lot, which is why I was saying with Outstanding it's almost 100% guaranteed you're gonna win all of them.
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