The Fighter is a fighting machine (as the name Fighter suggests). He has the most HP out of any class, and the ability to wear all the best armor lets him keep that HP for a long time. The Fighter also has access to most of the weapons in the game; his offensive power is matched by no other class (except maybe the BB). However all of the Fighter's strengths come from having the right equipment, and the best equipment is pretty expensive sometimes. The Fighter is the most expensive class to buy weapons and armor for, but that's more of a problem early in the game than later on. If you want an easy time in FF1, you pretty much have to take a Fighter.

The Black Belt is a pure fighter. He's the only character who can't use magic before or after class change, which is a minus in my book. Although he's not able to equip many weapons, and the weapons he can equip are very weak, the Black Belt's most powerful weapon is his fist. After level 7 or so, if you unequip the BB's weapon and let him use his bare hands, he'll start doing damage comparable to a Fighter. Because he doesn't require much (if any) equipment for most of the game, the Black Belt is cheap as dirt, and his extra armor and weapon slots can be used to store weapons and armor for other characters or magic-casting weapons like the Heal Staff. The Black Belt's weakness is his inability to use magic and his horrible defense, but if he has proper support from a White Mage, and you hide him in the back row of your party, the Black Belt might live long enough to be an effective fighter. (Sometimes.)

The White Mage's main purpose is to heal her comrades. She lacks physical strength, being able only to equip Hammers, and will never be an effective fighter. Likewise, the inability to use armor other than Bracelets and some minor accessories make her very vulnerable to attack. In spite of her weaknesses, however, the White Mage is indispensible in her unique power to heal and protect her allies. Even the strongest fighter will die pretty quickly if you don't have enough white magic to keep him alive; the White Mage's job is to keep the fighters alive long enough to do their job, and this she does with more skill than any other class. Another strength of the White Mage is her strength against undead. White Mages are the only character that gets to use HARM magic, and there are a ton of undead monsters in the game, enough to make HARM magic worth getting. Although the White Mage's spells will be expensive in the beginning of the game, they're well worth the investment, and she makes up for it somewhat in that she doesn't need expensive weapons or armor.

The Knight has all the skills of the Fighter and more. He has access to every piece of armor in the game, with exception of only a few, which suck anyways. He's also the only character who can equip the mighty Xcalber, the second best sword in the game. At high levels, with a good suit of armor and the right weapon, the Knight is a one man army, almost invincible. In addition to his physical strengths, the Knight has the ability to learn some white magic spells, effectively adding a low-level healer to your party. In terms of raw strength and defense, there's no one that beats a Knight.

The Master is exactly the same as the Black Belt. He gets nothing from class change. So if you liked the BB before, you'll probably like the Master too. If you hated him before, you'll hate him more now, because every other character gets a bonus from class change and the Master doesn't. The Master is still a pretty strong fighter though. In fact at very (very) high levels, the Master will do more damage bare-handed than a Knight with the Masmune. At level 50 the Master is by far the strongest character, in terms of physical attacks. He still doesn't get any magic, and he still doesn't get any good armor at all, and his HP progression isn't all that great, but if all you want is someone to punch stuff really hard, the Master is your guy. Just make sure you continue to hide him in the back row. Or give him the Opal Bracelet and a Ribbon, it's better than nothing.

Having mastered the healing arts, the White Wizard's healing magic is second to none. The White Wizard has access to all White Magic spells, including powerful 8th Level spells that no other class can use. Spells like LIF2, which brings a comrade back to life with full HP, is very helpful when fighting the powerful foes near the end of the game. FADE is probably tied with NUKE for the most useful damage spell in the game. The White Wizard's protection spells become more and more valuable as you fight more enemies with strong magic attacks. Although she's still not much of a fighter, the White Wizard is a great addition to any party.