There are six different characters to choose from in Final Fantasy: Fighter, Thief, Black Belt, Red Mage, White Mage, and Black Mage. Each character has his own strengths and weaknesses. After you get the AIRSHIP, go the the Castle of Ordeal and find the TAIL. Take it to Bahamut, the dragon king, and he will change your characters' classes.

Fighter

The Fighter is the basic warrior. Able to use most weapons and armor, he is best in the front of your party lineup where he can absorb most of the hits from monsters. He is a strong asset in combat with his high damage ratings as well. Only the most powerful monsters can withstand more than one blow from his weapons. On the downside, his armor tends to slow him down, and he tends to be the last character in the lineup to make his move. At the beginning of the game, buying weapons and armor for him tends to eat up a lot of your gold, although as the game progresses, you'll find better weapons and armor than are sold in the shops. The Fighter transforms into the Knight after a class change. The Knight can use most of the few weapons and armor that the Fighter cannot, including the Excalibur. The Knight also gains some White Magic spells from levels 1 to 3. This is a good, solid class for beginners, although experienced players will probably find it useful as well.

Thief

The Thief is a master of evasion. Of all the characters, he has the bast chance of running from battle, and from avoiding enemy attacks. The Thief is a fair warrior, about equal to the Red Mage. He has a pretty good selection of weapons as well, though there are a number he can't use. His selection of armor is relatively poor. After a class change, he turns into the Ninja, and greatly improves. He gains a much wider selections of weapons and armor including the Katana, which only he can use. He also gains the ability to use any Black Magic spell from the first four levels. The Thief is generally weak at first, but later becomes much more powerful and useful. This class is best for players who are somewhat more experienced, though a beginner could find it useful as well.

Black Belt

The Black Belt is a master of martial arts. Although he has the worst selection of weapons and armor of and warrior, his true strength is in unarmed combat. Unarmed, he can strike twice as many times than any other character in the game, inflicting a large amount of cumulative damage. He often kills most opponents with a single blow, and can inflict significant damage on the bosses. Combined with a FAST spell, this character can become the most powerful warrior in the game. Class change turns him into a Master, but there are no real changes in ability, and he is the only class in the game that cannot use magic at all. The Black Belt is a solid warrior, equal to the Fighter in terms of ability. However, he is often underestimated by players who only look at his poor selection of weapons and armor and lack of spells. He is a good alternative to a Fighter, and using a Black Belt can save money that can be used to buy items and spells instead.

Red Mage

The jack of all trades. Red Mages can cast both White and Black Magic spells. This gives him access to all the elemental damage spells, such as FIRE, LIT and ICE, and curative magic like CURE. Red Mages are fairly good warriors as well; not as good as the Fighter or Black Belt, but better than the Thief. They have a good selection of weapons and armor, second only to the Fighters. After a class change, Red Mages become Red Wizards, gaining access to some items and spells that they couldn't use previously. The Red Mage is best as a supporting character, depending on the type of party you're using. He can be used to give some magic to a party composed mainly of fighting classes, or as a warrior in an all magic-using party. In a party of mixed types he can serve multiple roles as needed: as a fighter, a healer, or an offensive magic user. This class is usually best for players who are familiar with the spells and their effects, and who like using magic. Alone of all the classes, the Red Mage is probably best suited for single-class parties.

White Mage

The White Mage is a master of White Magic, used for healing and protection. The use of White Magic is her only real strength; she has the worst weapon selection in the entire game. After a class change, she turns into the White Wizard, gaining the ability to use some spells and items she couldn't use before. Lacking offensive magic and combat abilities, the White Mage is best for healing magic. A party without access to White Magic will have a difficult time getting through the game, and will likely have to use a large amount of HEAL potions.

Black Mage

A master of Black Magic, used for attack. The Black Mage's main purpose is to cast powerful elemental damage spells which can often kill or at least seriously weaken a group of enemies. He also has spells which can incapacitate or instantly kill enemies, although these tend to be less reliable. His weapon selection is poor, although he should rely on attacking with his spells first unless the enemies are weak. He should also go at the end of a party, since his hit points are the lowest in the game. After a class change, he becomes a Black Wizard and gains the use of spells and magic he couldn't use before. A Black Mage is good if you prefer to use magic in your strategies, otherwise, you probably won't find much use for the character.

Courtesy of Final Fantasy Classics.