Q:

Warding Bond: What is the Order of Operations for calculating cleric damage taken?

The warding bond spell allows a support character (cleric) to buff another creature (Basic Rules p. 105):

While the target is within 60 feet of you, it gains a +1 bonus to AC and saving throws, and it has resistance to all damage. Also, each time it takes damage, you take the same amount of damage.

What is the Order of Operations used to arrive at the final damage that the cleric receives as his share?
Resistance rules brought this up (Basic Rules, p. 75) as we hoped to Ward a raged Barb - MEGA Tank - until our DM reminded us that you don't double stack like resistances (PHB, p. 197).

If a creature or an object has resistance to a damage type, damage of that type is halved against it.

I'll be buffing our Paladin.
Two cases:

Weapon damage (a hammer blow, a claw strike, gored by a gorgon …)
Damage where a saving throw versus magical damage (usually a spell or spell like effect) is required.

Case 1.  I stay 30' behind Paladin.  Giant scores a hit, doing 16 points of bludgeoning damage.  Warding Bond (resistance) reduces that to 8.  I take 8 HP.
Case 2.  The Wizard whom the Giant serves fireballs the Paladin on his action.  (I am outside blast radius).  Rolled damage is 24, Fire.  Paladin has resistance to all damage (from Bond) thus 24 is halved to 12.  He rolls a saving throw, and succeeds with a 17.  He takes 6 damage.  I take 6 damage.
My view is that we can't assign damage to Cleric until we know total damage to Paladin.
Paladin and I weren't sure about the case of fireball: should it be different from the Giant's hammer, since you don't get a save versus melee weapon damage?  With fireball reduced damage (from resistance) at 12, do I take 12 unless I too save versus fire as the Paladin did?
I don’t think so.  It seems to violate the KISS principle.  But, the Bond ties the cleric magically to the Paladin.  Is magic going to follow that path of least resistance?
Do I have the order of operations right?

First resolve all damage to Paladin.
Then apply that amount to Cleric.

Is there something we missed that would support the other order of operations?

A:

The short answer is that your Order of Operations is correct for both the attack and the Fireball. The rules use the phrasing "takes damage" consistently throughout.
The example given in the Damage Resistance and Vulnerability section (page 197 of the PHB), answers a lot of your questions.

For example, a creature has
  resistance to bludgeoning damage and is hit by an attack
  that deals 25 bludgeoning damage. The creature is also
  within a magical aura that reduces all damage by 5. The
  25 damage is first reduced by 5 and then halved, so the
  creature takes 10 damage.

So, the raw damage is phrased as "an attack
that deals 25 bludgeoning damage". Then all the calculations are done, then the final result is phrased "the
creature takes 10 damage". Warding Bond says that

each time it takes damage, you take the same amount of damage.

Therefore, the Cleric will take the actual amount of damage that was applied to the Paladin's hit points after all the resistances and saves were calculated.
Fireball won't change the order of operations, since the Dexterity save determines how much damage the Paladin takes. For proof, we can go to Fireball itself:

A target takes 8d6 fire
  damage on a failed save, or half as much damage on a
  successful one.

Or, to put it differently, a target takes half as much damage on a successful save.

