brainstorming

Characters have four ability scores, with 7 points to distribute amongst them
Power +0 : strength, stamina
Quick +0 : reflexes, agility, speed
Moxie +0 : willpower, personality, grit
Valor +0 : bravery, fortitude, luck

Originally I was thinking that these abilities would simply play off the standard ideas of having an attack roll, an armor class, and hit points.
Power would add to a base Attack of +0
Valor would add to a starting pool of 10 Hit Points
Armor Class would be on an ascending scale, starting at 10 and going up with Quick

I tried to break the classic four classes down into two traits and if every player would be allowed to select two traits, they could mix and match class characteristics. I had a hard time coming up with something simplistic, so I just created a list of categories for modifications to Attack and HP.

CHAMPION = add Valor to Attack
PUGILIST = add Power to HP
HOOLIGAN = add Quick to HP
RAKE = add Quick to Attack
APOSTLE = add Moxie to Attack
HEALER = healing ability (roll using Moxie)
MAGUS = add Moxie to HP
ENCHANTER = magic (magic uses HP to cast)

As I examined the math of these traits I realized that maxing out Quick and picking the Hooligan and Rake traits would make an uber-character. There was no reason to create any other combination unless you wanted to heal or cast magic. I started to revise how these secondary abilities would work.

Instead of having a base starting score for Armor Class and Hit Points, I devised a calculation that would force players to truly examine where they would be putting their points. I wanted to force a "pure" Wizard concept character to put points into other abilities, instead of just maxing out Moxie, and I wanted a "pure" Fighter concept character to be forced to examine Moxie's role in their secondary stats.

base Attack score would be a total of Power and Valor together
Armor Class would be the total of Quick and Moxie added together and doubled
Hit Points would be the total of Valor and Moxie added together and doubled

With these numbers I would have to change how points were distributed, and I couldn't allow for an ability score of +0 otherwise somebody might accidentally start with a 0 HP character. All characters would start with +1 in each ability score and then get 7 points to distribute on top of that.

The real kicker to all of this is that I wanted my math to work out with rolls being made using 2d10 added together instead of the traditional 1d20. Partially this was because I wanted a simplification of the target numbers for rolls, and partially it was because I wanted the target number to be rolled to never exceed 20.
Target Numbers would have to: 10, easy; 15, difficult; 20, impossible

The last thing I came up with were the spells for Wizards, which I always intended would cost Hit Points to cast and some spells would require Moxie rolls to succeed.
Destroy Chaos: 1 HP, roll Moxie vs TN 10, destroys any Chaos creature with less HP than the Wizard
Disarm Trap: 1 HP, no roll
Light: 1 HP, no roll, +1 HP permanent
Magic Missile: 1 HP, no roll, hits one target, 3 damage
Fireball: 2 HP, no roll, hits one target, 1d10 damage
Necrosis: 3 HP, roll Moxie vs target's AC, reduces Attack and Quick to +0 (re-calculate AC = cut in half)
Teleport: 4 HP, roll Moxie vs TN 10, +1 HP no roll
Death Bolt: 5 HP, roll Moxie vs target's AC, kills target

I wanted to simplify the Cleric's ability to heal as well. I didn't want any roll to be involved but I wanted a cumulative cost for the use of a multi-purpose power. This is what I settled on...
Healing: heal 4 HP, cure poison, or prevent death (if body not destroyed)
Cleric must touch target of the healing, each use lowers all of the Healer's ability scores by -1 (including Armor Class and Attack), all lost points recovered after rest

Here are examples of characters that I wrote up in the way I would want to play each class...
Power +1 , "zero level"
Quick +1 , Attack +2
Moxie +1 , AC 4
Valor +1 , HP 4

Power +2 , planning on being a WARRIOR
Quick +2 , Attack +7
Moxie +2 , AC 14
Valor +5 , HP 14

Power +1 , planning on being a ROGUE
Quick +6 , Attack +2
Moxie +3 , AC 14
Valor +1 , HP 8

Power +2 , planning on being a CLERIC
Quick +2 , Attack +5
Moxie +4 , AC 10
Valor +3 , HP 14

Power +1 , planning on being a WIZARD
Quick +2 , Attack +2
Moxie +7 , AC 6
Valor +1 , HP 16

Looking at how the numbers break down, the only thing left would be to design the classes (instead of picking two traits which could be min-maxed)
WARRIOR = add Power to HP, add Valor to HP
ROGUE = add Quick to HP, add Moxie to AC
CLERIC = add Valor to Attack, healing (uses Moxie and Valor)
WIZARD = add Quick to HP, magic (uses Moxie and HP)

With these additions the characters change into
Power +2 , WARRIOR
Quick +2 , Attack +7
Moxie +2 , AC 14
Valor +5 , HP 21

Power +1 , ROGUE
Quick +6 , Attack +2
Moxie +3 , AC 17
Valor +1 , HP 14

Power +2 , CLERIC
Quick +2 , Attack +8
Moxie +4 , AC 10
Valor +3 , HP 14

Power +1 , WIZARD
Quick +2 , Attack +2
Moxie +7 , AC 6
Valor +1 , HP 18

The really glaring things to me are with the Warrior, he does not have much of an advantage outside of the boost to Hit Points and I intended Power to be an important ability but the math forces Valor to become prominent. Others might notice that Wizards have lots of Hit Points, but that's because their spells require HP to use.

A quick breakdown of the mathematics
Attack = Power + Valor
AC = Quick x2 + Valor x2
HP = Moxie x2 + Valor x2

These are just ideas at the moment, but this is where my ideas have been trailing off to.