Stongest Class

Try fighter , paladin(good hp) , defender for melee and for ranged try the sniper(viera) doubleshot ability from behind it does loads of damage.

It's all coming back to you. If you want melee, pick fighter or paladin. You may want to recruit some bangaa(His job almost all melee). If you want ranged attack, recruit some Viera because they have sniper job. If you want magic, recruit some nu mou! Nu mou have the best magic job among all race.

Hume: Parivir: As soon as you learn the blade techniques; such as Shimmering Blade, Skyfury Blade, etc. They deal 2x the damage of a normal attack, they don't take any MP to use, and they come with special effects.
Bangaa: Cannoneer: This job has a whole bunch of support abilities that let you attack twice, increase attack, accuracy, etc. The down side is that you must be a Cannoneer in order to use the abilities.
Moogle: Fusilier: They come with so many attacks with special effects; IT;S AWESOME!!! I love moogles so much, I have a whole clan full of moogles, and I can beat enemies 15 levels stronger than I am; mainly using status effects. :-)
Nu Mou: Arcanist: With each level up, you get, like, 10MP, and by level 45, my arcanist had 415MP!! And, they can drain MP or HP, it only costs you 8MP, and you get healed!
Viera: Assassin: Super fast and hit hard, with awesome spells. But, there are 2 downsides: They don't gain a lot of HP, and the spells cost a lot of MP.
Gria: Raptor: They gain a lot of defense, their weapons have a lot of attack power, and their 'Crush' abilities are super sweet.
Seeq: Ranger: Rangers are super awesome as soon as you learn the 'Mirror Items' abilities, and the 'Item Lore' passive ability. When you use 'Mirror X-Potion', you do 400 damage with the same accuracy as if you did a normal melee attack. (99%)

In my opinion, the strogest class melee-wise would either be parvir for hume, and master monk for bangaa, both know awesome abilities and deal massive damage.

Parvir for humes of course
Dunno bout bangaas...
Nu mou illusionist kuz they can hit everyone everywhere
And for vierra summoner

And also sage for nu mou they are savage

Ok I'll give you my favorite for each race and this includes secondary abilities reaction abilities and passive abilities

Hume-Parivir (second ability pugilism reaction strike back passive dual wield)
Bangaa-trickster (second ability martial arts reaction blink counter passive unscarred)
Vierra-Assasin (second ability sharp shooting reaction return fire passive doesnt matter)
Nu Mou- don't really have a favorite... Sage and alchemist I guess
Gria-Ravager (second ability devastation reaction strike back passive attack up)
Moogle-Fusilier (second ability onslaught reaction critical:vanish passive concentration)
Seeq-Lanista (second ability brutality reaction blink counter passive death strike)

For humes I would recommend either the fighter or the ninja, mostly because of the dual-wield ability. If anything, you can do a black mage as well as a seer for tons of damage. For ranged, make them a hunter for the Ultima shot ability later on. For bangaas, in the beginning i'd use the dragoon for massive damage w/ the jump ability, and have white monk abilities as a secondary ability, or vice versa. When you get it, get the master monk class w/ white monk abilities. I'd go either summoner or red mage for viera, nothing for seeq (they're almost worthless) and either ravager or raptor for gria. Nu mou illusionist with black mage abilities or black mage with time mage abilities.

The strongest possible class is a hume paladin equipped with the sequencer. Then you make the secondary ability the parivir skills, and the passive ability geomancy. That way, you deal x4 damage with the elemental blade attacks, and you're using the most powerful weapon in the game to boot. With this setup, you can OHK pretty much any enemy from behind.

If you consider character-specific classes, the Heritor (Adelle's hidden class) is the strongest. Otherwise, a Hume paladin with the Sequencer (and another powerful knightsword if he can Dual Wield) is the best.

Well, I can say it truly without any doubt, use the abilities of the ninja "ninjutsu", and be on the "seer" job, then train that class, train the "magic frenzy" and voalà, you'll never lose; if you don't lose your focus