The previous post is very informative for raising stats, there are also food benefits, depending on what you feed your chocobo.
In no particular order, the chocobo food is listed below. Most of them you can get from the AH, or it can be gardened and the salads can be made with cooking.
■Tokopekko Wildgrass is effective for illnesses.
■Garidav Wildgrass is for stomachaches.
■Gausebit Grass is good for wounds.
■Vomp Carrots increase Strength and Endurance by 0.5.
■San d'Orian Carrot - Raises Endurance by 1 and lowers Strength by 1.
■Zegham Carrots Increases Discernment and Receptivity by a small amount.
■Cupid Worms increase the chocobo's affection by a substantial amount (about +3 Affection) and lowers one of your highest stats by a small amount. This effect is canceled when the bird is perky or in high spirits.
■Gregarious Worms - restores about 1/4 the chocobo's energy, completely fills chocobo.
■Parasite Worm - lowers a random stat and allows your bird to eat more. Also believed to erase one of its abilities, but is still to be confirmed. Also, the idea that worms permanently freeze stats is false. The reason this myth came about is a person would feed the bird this near day 64, which is when food no longer has any effect on the chocobo. Days after that are meant for learning abilities.
■Lethe Potage - Will erase abilities. Amount needed to feed varies from 1 to 6, effect is immediate.
■Gysahl Greens satisfy the chocobo's hunger (moderate amount) and increase the chocobo's affection slightly.
■Sharug Greens satisfy the chocobo's hunger (moderate amount) and increase the chocobo's affection dramatically. May take up to 5 to completely fill a starving chocobo.
■Azouph Greens satisfy the chocobo's hunger (highest amount) and increase the chocobo's affection dramatically. 2 will completely fill a starving chocobo.
■Chocolixir will restore the chocobo's energy to full (provided it is given when the chocobo is not full) And completely heal all status ailments. Fills a starving chocobo halfway.
■Chocotonic - wakes up sleeping chocobo, slightly lowers affection. This was introduced as a way to fix the bird from the sleep glitch.
■Celerity Salads are effective for most status abnormalities, restoring instant health to the chocobo. Also increases Discernment by small amount. Does not increase Receptivity though.
■Carrot Paste is feed for chicks that raises physical attributes, and fills the chick up rapidly, but lowers Discernment.
■Herb Paste is feed for chicks that cures illness.
■Vegetable Paste is feed for chicks, and increases affection.
■Worm Paste is feed for chicks, and heals it slightly and increases energy, while dramatically increasing affection, but lowering its stats.
■Lethe Consomme - Will erase abilities. Amount needed to feed varies from 1 to 6
Good luck with your chocobo raising!!! It's time consiming and can get expensive but it can pay off in the end.