Recommended races: Tarutaru and Hume
Black Mages are the experts of the Black Magic and all other spells that are utilized for dealing damage. Black Mages are said to be the master of damage, though this is a phrase which should be carefully understood. Black Mages have the widest variety of damaging spells available to them, some of which can hit for staggering amounts of damage. However, not all players see Black Mages as being the most overall damaging job, despite their tremendous powers. This is because in longer fights, the Black Mage can run out of MP (Magic Points), meaning that eventually other jobs can outdamage the Black Mage. This being said, a good Black Mage can make a fight end a lot faster.
In some ways, Black Mages are best compared to Monks. Both jobs are good at dealing large amounts of quick damage, but do not do as well absorbing damage themselves.
It should be noted that Black Mages do all of their damage at range. The favorite position of a Black Mage is standing well behind a few Warriors or Monks (or anybody else that can keep the monsters from getting to them). Because of this, most Black Mages prefer to party when they hit mid to high levels. If you want to deal impressive amounts of damage without the risks of melee combat, black magic is your best choice.
Black Mage magic is primarily damaging magic, with some disabling spells as well. Black Mages can not cast healing magic. Note that all mages need to learn a spell before they can cast it. Learning a spell involves buying the spell scrolls (similar to how warriors must buy weapons) and then learning (using) it to put it into their spell book.
Black Mages are limited to clubs, staves and ranged weapons.
Black Mage combat skills: dagger, club, staff, throwing, guard, evasion, enhancement magic, enfeeblement magic, elemental magic, and dark magic.
Recommended races: Tarutaru, Hume and Mithra
Where most jobs in FF XI specialize in doing one thing, the Red Mage is a generalist who learns to do a bit of everything. Want to cast both healing and damaging spells? Want to do so in armor and using a sword? If so, the Red Mage is for you.
The Red Mage is a fighter / mage, able to use both swords and spells. The Red Mage gets some of the healing magic of a White Mage, some of the destruction magic of a Black Mage and a little bit of their own magic thrown in as well. This being said, the Red Mage learns most of their spells at higher levels (i.e. later) than White / Black Mages learn theirs.
Red Mages are good (but not great) in melee combat - their combat skills are roughly equal to those of a thief. Red Mages are not as good at mitigating damage as a Warrior or a Monk.
Red Mages have strong defensive skills: they get both Shield (allowing them to block attacks with their shield) and Parry (allowing them to parry attacks with their weapon).
Red Mages can solo fairly well. This is due to their good armor selection, good weapon selection and offensive / defensive spells. There can be times, however, when Red Mages have trouble finding a party - many parties want a specialist as opposed to a generalist.
Red Mages can wear most armor (as opposed to Black and White Mages that have a more limited armor selection). They also have access to a wider variety of weapons than the Black and White Mage. This can make Red Mages more expensive to play, as they are constantly upgrading their spells, their armor and their weapons.
Red Mages get all types of magic, as they draw from the spell lists of both Black and White mages (and a few of their own unique spells as well). Note that all mages need to learn a spell before they can cast it. Learning a spell involves buying the spell scrolls (similar to how warriors must buy weapons) and then learning (using) it to put it into their spell book.
Red Mage combat skills: dagger, sword, club, staff, archery, marksmanship, throwing, evasion, shield, parry, divine magic, healing magic, enhancement magic, enfeebling magic, elemental magic, and dark magic.