About A Spheres
They generally lean toward improving attack capabilities.
Keywords for the abbreviations below are referenced at the bottom
What is best?
Every character is different, but there are some general rules.
ATK is best to overcome high defense or when skills scale off ATK (this gains value in the Lufenia+ era)
BRV DMG increase is best to overcome BRV DMG reductions, especially vs. low defense (these tend to be more valuable in the BT era)
mBRV & iBRV are marginal effects and are good filler spheres
Overflow A spheres
Best for characters with many AoE skills that tend to cap
(a few examples: Lann & Reynn, Strago, etc)
BRV DMG A spheres
These are among the best spheres in the game, and best for most attackers, especially those with high ATK or ignore DEF based kits.
ATK A spheres
These are the defacto A sphere, and are good on every character with an A slot, just make sure your character can trigger it!
mBRV & iBRV A spheres
These are the worst A spheres available, and generally should not be placed on any characters unless they have no BRV hits in their kit and specifically benefit in a strong way from improvements to their MAX BRV stat.
Other A spheres
These spheres are best stated as weird. Perhaps a character benefits from this effect, but it's unlikely that the benefit is better than BRV DMG or ATK. The biggest stretch may be Galuf wielding Iroha's sphere. Balthier's sphere is the worst A in the game, and Cinque's is a worse version of Iroha's.
Keywords used under character images:
broken - when attacking a broken target or breaking them
vs broken - when attacking a broken target
on break - when breaking a target
crit - when dealing a critical hit
weak DMG - when dealing weakness damage
debuffed - when any enemy is debuffed
vs debuffed - when attacking a debuffed target
on evade - after dodging an attack
vs not targeted - when attacking an enemy not targeting that character
ST BRV or AoE BRV - when dealing single target BRV damage or AoE damage. A normally AoE attack vs a single target counts as an AoE BRV attack