Mechanically, not at all. You’re free to make the choice in any order you wish.
At endgame, it will be optimal to choose the order that puts the most into the buffs you are working with, although that may be different depending on your raid composition.
The other reason to choose is that Garuda and Ifrit have some restrictions on their spells with long cast times, so make sure you can stand still to actually cast them when you enter those phases.