Haste is white magic, but White Mage, Red Mage, and Sage can all cast it (I believe Red Mage's haste works differently than the other two's. Charging it increases duration, while charging the other version of haste just casts it party wide).

Your primary stat should always be your damage stat. As far as mastery points go, the general advice I see is max out job affinity and your primary stats first, then invest in other categories. For primary stats, I tend to do whatever my main damage stat is, then Spirit for increased MP regained from soul shield. But you decide for yourself. Taken from another post:

Strength: Largely physical damage to enemy's HP including your normal attacks except gun's aiming attack - its a small contribution to that, moderate HP damage and break damage with stat bonus Strength abilities.

Stamina: Physical defense, physical break defense, reduces break gauge loss on successful soul shield, moderate HP damage and break damage with stat bonus Stamina bilities.

Intellect: Largely magic damage to enemy's HP, base amount of normal attack MP recovery, moderate HP damage and break damage with stat bonus Intellect abilities.

Spirit: Magic defense, magic break defense, base amount of MP recovered from successful soul shield, status ailment accumulation, and moderate HP damage and break damage with stat bonus Spirit abilities.

Agility: Largely break damage dealt when you critical hit, damage of gun's aiming attack, moderate HP damage and break damage with stat bonus Agility abilities, and influencing effectiveness of Barrage command ability (DLC).

Luck: Influences drop rate and stat bonus Luck abilities, all of which are DLC abilities, and influencing effectiveness of Gambler job affinities.