You could breed your chocobo to increase its pedigree and stats cap. When I was breeding mine I only leveled max speed and stamina to get them to rank 40.
You can do challenges to unlock manuals but they are not easy. This way you can teach your favorite ability just buying the manual. (https://www.reddit.com/r/ffxiv/comme...lenge_rewards/)

My current chocobo stats are:
Max speed 500/500
Acceleration 330/500
Endurance 500/500
Stamina 500/500
Cunning 420/500
I ignore acceleration because I use Super Sprint.