The Archmage must have three spell levels in all four of the previous spellcasting classes. The Archmage is also strictly required to win The Destiny Knight, not the least because only an Archmage can become the eponymous Destiny Knight.
A "true" Archmage is a character that has learned all seven levels of spells in all of the other casting classes Conjurer, Magician, Sorcerer and Wizard. In The Destiny Knight and The Thief of Fate, the Archmage is a class of its own, and gain an additional seven levels of spells. FYI: In the second two games, the code for the "Godspell" is ZZGO.
Archmage Development in Tales of the UnknownEdit
In Tales of the Unknown, an Archmage is not a class of its own, and there are no Archmage spells: "Archmage" simply refers to a character who has learned all seven levels of spells in the four casting classes. As spellcasting characters can only start in the Conjurer or Magician classes, and both of these classes gain levels faster than the Sorcerer or Wizard classes, you may be best served by following this progression of class changes:
You may be tempted to push one (or both) of your casters through the other starting spellcasting class to have redundancy of spells for your casters (it's nice to be able to have two casters who can cast utility spells like Trap Zap, Ybarra's Mystical Coat of Armor, Kiel's Magic Compass, Major Levitation, Greater Revelation, or Restoration) and to get more spell points/hit points immediately: however, you may want to re-think that idea.
Getting the Most Out of Your Experience PointsEdit
In the end game, ending your spellcaster's class progression on Conjurer or Magician makes it easier to get you more spell points and hit points for a given amount of Experience, not to mention increasing the power of spells that are affected by caster level, increasing your Spell Resistance (and thus reducing the enemy's chance to resist your spells!). This can save your skin when navigating hazardous dungeons like Mangar's Tower! Further, if you're going to transfer your characters from Tales of the Unknown to The Destiny Knight and/or The Thief of Fate, the additional HP and SP will make a huge difference.
After Level 13, Conjurers and Magicians level every 230,000 points, compared to 400,000 for Sorcerers and 1,300,000 for Wizards, a difference of 170,000 points for ending on Sorcerer (73% slower!), and a difference of 1,070,000 points for ending on Wizard (465% slower!). While Sorcerers and Wizards do get 1-8 Hit Points per level vs. 1-4 for Conjurers and Magicians, the fact that end-game Conjurers and Magicians level 4 times faster than Wizards could more than make up for their lower HP per level. Depending, of course, on your play style.
Spell Resistance = Spell EffectivenessEdit
In the end game of TotU, Spell Resistance value is a major factor in determining the effectiveness of your casters versus the most powerful monsters in places like Mangar's Tower. With a potential maximum resistance value of 22, your spellcasters will have to have a decent level of experience to reliably break through their defenses. While Wizards have slightly better Spell Resistance than other casters of comparable level, it turns out this can be easily compensated for by gaining an extra couple of experience levels.
Experienced players can easily win the game with characters that have racked up as little as two million experience points, but they don't expect to come out of the more difficult encounters unscathed. If you like to grind up your characters until you are almost invincible, this will probably be easier done with Conjurer or Magician as your ending class. Unless you like to visit the Spectre in the cats for easy money and levels.
Comparison: Assuming 5.8 million experience points gained by each party member, and melee members at level 36-34, a TotU Archmage ending on Wizard is Level 16, with a spell resistance score of only 18 (assuming 18 Luck and equipped with a Luckshield)... while an Archmage ending on Magician with the same 18 Luck & Luckshield is already Level 28, and has a spell resistance value of 23!
Knowing that the end-game monsters such as the Demon Lords accompanying Mangar have a potential maximum spell resistance of 22, having a spell resistance of 23 means your damage-causing spells are at full effect at all times! On the other hand, having a value of 18 would mean an only 3-in-8 chance of causing full damage, a 4-in-8 chance of them only taking half damage, and a 1-in-8 chance of doing no damage at all - not good, unless you're competent with more complex battle tactics.
But My Accessories!Edit
Another reason you may want to end up with a Wizard as your final class in TotU is that there are some items later in the game that wizards can wear or use that Conjurers and Magicians can't. This includes weapons like the Spectre Snare and Spectre Mace, armors such as the Lorehelm and Mthr Gloves, and the Elf Cloak. It is difficult to get the armor class of a Magician or Conjurer down to LO, but not hard for Wizards. If your party is caster heavy and you have casters on the front line, you may want to reserve Wizard for their final class.
There is no game-mechanics-based reason to want to end your progression on Sorcerer: there's no specialist gear for Sorcerers that Magicians and Conjurers can't wear, and in terms of HP/SP gain, while Sorcerers do get a 1-8 base HP increase, and level much faster than Wizards, you'll get more of both from progressing as a Conjurer or Magician due to the cumulative Constitution and IQ bonuses. Although there is nothing stopping you from racking up more HP and SP as a Magician or Conjurer before switching classes, you lose all the bonuses of higher level when you switch. These are Spell Resistance, including the ability to run from encounters (in the rare case your caster is your front line character), and battle initiative.