Here's a brief rundown of the jobs:
Squire: basic starting job for the warrior path. Squire itself isn't a great job, but it has JP Boost which is good to get early on to get more JP for your characters. Move +1 isn't bad either.
Note that Ramza's Squire job set is unique, he gets several good party support abilities the basic squire doesn't. His equipment is also slightly different which means he can't equip axes (which suck anyway).
Chemist: Unlike Squire, Chemist stays useful much longer because they can equip guns. Your key abilities here, besides the individual item skills, are Safeguard and Auo-Potion.
Knight: Knight is an ok job, particularly earlier in the game, but they're less useful later. First, they can't equip clothes and hats, so they lose out on much of the PA boosting gear. Second, their job set isn't that great. They are the only generic job that can equip Knight Swords, but meh. You get some good story characters that can equip Knight Swords in their base job anyway (like Ramza who can wear all that nice stuff that boosts his PA). Parry is an ok reaction ability and Equip Sword is useful for some of the unique characters.
Archer: Archer's an ok ranged attacker. The main ability here is Concentrate, which lets you ignore enemy evasion.
White Mage: The basic FF healer job. You get the usual healing spells here, plus Protect and Shell, and Holy.
Black Mage: Another classic FF job. This has the usual elemental damage spells, plus Death, Flare (Holy is better though), and Toad. There's also Arcane Strength for boosting your MA.
Monk: This is a pretty good job. You get a good mix of offensive and support abilities (I usually use this as Ramza's second skill set). There's also Counter, which is a decent Reaction ability, and Hamedo which is very good when used for the right battles. First Strike lets you counter a weapon attack by attacking before the attacker attacks, but it's pretty useless against monsters.
Thief: not a strong job on its own, but it has a good set of skills that you can combine with other jobs. First, there's the stealing abilities which you can use during certain story battles to grab rare or unique gear. Move +2 is one of the better movement abilities especially for battles that take place on flat open maps with few obstacles. Poach is important for getting some rare pieces of gear.
Time Mage: This gives you Time Magic, so you get stuff like Haste and Slow, as well as damage spells like Demi and Meteor. The job itself isn't great on its own but you get several very good secondary abilities: Mana Shield, Swiftness and Teleport.
Mystic: Mystic is a very good caster. It uses a lots of status effect spells, and unlike a lot of games, these can be pretty effective. You can petrify enemies or turn them into chickens, or mess them up in all sorts of fun ways. Not a lot of direct damage from spells, but there's Life Drain (apparently called Invigoration in the PSP version) which is pretty good on its own, and it can be used pretty effectively against bosses. There's also the fairly useful Defense Boost ability as well. Mystics also fight fairly well for casters, they use staffs and sticks as weapons, both of which calculate damage based on the character's MA rather than PA. So this job is used to neutralize an enemy with negative status effects, then you poke it hard with a stick until it's dead.
Geomancer: Geomancers can use the terrain to make attacks on enemies. They're also a good base for characters that use both physical and magical attacks because they have a both a decent PA and MA score. They also have one of the best equipment sets in the game: swords, shields, clothes (some of which boost PA), robes (some of which boots MA), and hats (which can boost PA, MA and/or Speed). And they get Attack Boost as well.
Dragoon: another classic FF job, these are the jumping spear guys.
Summoner: another classic FF job. You summon various creatures that either inflict damage or use a healing or support effect on the party. It also gets Half MP.
Orator: This job has a variety of skills it uses by talking to enemies. It's mostly a support job, but there's three main abilities: you can invite enemies to join your team, and you can permanently adjust your Brave and Faith scores. It's also the only job besides Chemist that can equip guns and it gets the Equip Gun ability. Otherwise, it's a job that's only useful in certain situations.
Samurai: The Samurai uses katanas to either damage enemies or heal/support the party. This is another job which isn't great on its own, but which has abilites that are very good combined with another job. Since the abilities are MA dependant, it's often good when combined with a Black Mage for the damage potential or a Geomancer which can equip MA boosting gear (unlike the Samurai). Note that katanas have a small chance of breaking, so be careful when using the rare ones. There's also Blade Grasp which lets you avoid nearly any physical attack in the game.
Ninja: This is the fastest job in the game. Ninjas can dual wield, which can be very powerful when used with other jobs. There's also Abandon, which is one of the best reaction abilities in the game. It basically doubles your Evasion, and it's a passive ability which is always active. It also isn't dependant on Brave either, so it can be effectively used by a character with a low Brave score.
Arithmetician: Arguably the most broken job in the game. It's also the slowest job in the game, but it can use its skills to cast certain magic spells the character has learned without any casting time, without MP cost, and at unlimited range. Did I mention how utterly broken this job is?
You don't use Arithmetician on its down because of how slow it is. You use Math Skill with another casting class to get access to most of the White/Black/Time/Yin-Yang magic you've already learned. It doesn't calculate some of the most powerful spells, but since you're casting a spell instantly for free anywhere on the battlefield, it's a fair trade-off. The only downside is that the calculations target eveything equally, both enemies and allies. Here's the various caster combinations:
Black Mage + Math Skill: Black Mage has the highest MA in the game, so this gives you the best damage potential.
White Mage + Math Skill: White Mage is generally the fastest caster in the game, so you get more turns.
Mystic + Math Skill: Mystics fight better than the other casters, so this can be useful when you can't make a calculation that only targets enemies.
Summoner + Math Skill: You can't calculate summons, so this gives you the biggest possible selection of spells in the game.
Time Mage + Math Skill: no real reason to pick this unless you want to cast Meteor (which can't be calculated).
Bard/Dancer: These jobs are similar, but are gender restricted, only males can become Bards, and only females can become Dancers. Bards have abilities which heal or buff your entire team, while Dancers damage or inflict statuses on enemies. Since there is no range limit, you can keep them at the back of the battlefield while the rest of your party fights. The Bard gets Move +3, but Dancer is stuck with Jump +3 which is junk when both of them get Fly.
Mime: this is probably the hardest of the jobs to use, but it can be very powerful when used right. A mime doesn't have any abilites and can't equip anything, but it repeats any action your characters make that isn't part of a unique job set. To use it right though, you have to be very careful about how you position it. How does this work? Say one of your characters attacks an enemy in front of him. The mime will also attack whatever is in the square in front of him. If you cast a spell, the mime will cast the same spell, in the same direction and at the same range. This get powerful when combined with Arithmeticians, Dancers and Bards, because the mime will repeat whatever calculation, dance, or song the character just used, and remember these affect the entire battlefield.
Also, NPC "Named" character's rarely stick around and usually end up fighting against you, so if you build them up, it will come back to haunt you, however if your take their stuff, some of it is really good.
