Okay, so not totally random, but here is a method I propose that might be interesting for choosing characters & starting gear (if everybody is okay with it in your group of course).
I know there are people who have developed systems for randomly generating dungeons (even without the need for Zargon) but this is more basic.
Player Order:
Each player rolls 1d6. Highest number goes first then next highest, etc. (in the case of a tie, roll again and these go in order from high to low).
Character Selection:
For this you can use an 8 sided die (Or a 10 sided die, but with adjustments).
First the player is given the option to choose to play as Zargon. If they decline, they roll a die (if they pick Zargon, they pass the die to the next highest roll from above).
1 = Barbarian
2 = Dwarf
3 = Elf
4 = Wizard
5 = Mystic
6 = Paladin
7 = Cleric
8 = Ranger
9 = Roll Again (unless you have another character class!)
0 = Roll Again (unless you have another character class!)
(if you have more, maybe a 12 sided die would work...)
If no dice, a game spinner with the numbers on it would suffice. With only four choices one could lay down four standard playing cards from the four traditional suites. Spades, Hearts,
Diamonds, or Clubs. Assign each to a character class. Yes, I know four sided dice exist...
If no one has selected Zargon by the end, the last player must be the Evil Wizard.
Once all characters are chosen for the group, we move on the the gear phase.
Equipment Selection:
Highest roller draws a random card from the "Equipment" Deck (a deck consisting of one card for each piece of equipment from the armory, and a few dupes for helmets, shields, daggers, etc).
Upon drawing the card, they can either keep it, or pass it to the next highest roller.
Once the player has two items, they are done and the next highest roller has a turn.
If a player already has two cards, they are "done" unless they choose to pass one to the next highest roller down the line, then they get to draw a new one. If they don't like the card they draw, unless the next highest person wants it (and is willing to pass their other card to the next person for it) they will have to keep it.
The only exception being if it is a piece of equipment they can't use (ie: Plate Mail for the Wizard, a Battle Axe for the Cleric, etc).
Once the gear is distributed, the players have a chance to negotiate (trade) items between themselves, but then the quest begins!
I thought about having a "random quest" option too, but here I think Zargon knows best. There are just too many to choose from, and some would be pretty tough starting from the beginning.
Optional:
Everybody gets a draw from the Combat Cards deck. And/or the Potion Cards deck.
Random Monsters? This would require a lot of cards, but say a deck of "monster cards" for Zargon to draw from when placing monsters. Could become unbalanced though... (though it would be a wicked idea for a "Wandering Monster" in the quest).