You absolutely want to get Haste and Hastega as fast as possible.
Support abilities don't do damage but they are just as vital as attacking abilities. It includes spells like Haste, Esuna, Reflect, and many others. A lot of them are part of the White Magic arch-type, but there are some other ones.
Tidus is the best option as his Sphere Grid has
it fairly early in the game. You want to rush towards this as soon as possible. It will be extremely helpful against tougher bosses.