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Most Important Stat

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Okay, so let me start this off by saying this; I am new to WoW but I am 100% aware that Strength is the most important stat for Warriors when talking about the major stats.


Now let's get started, as stated before I am new to WoW and I've decided to play a Warrior, specifically Arms mainly because I tried Fury and for whatever reason  2 weapons didn't seem to outdamage Arms having 1 (feel free to clear that up if you want but that's not the point of this topic).  What I can't seem to figure out is which stat in the melee character information window is the most important to increase damage between Damage, DPS, and Attack power. I've asked people and there are 3 types of people so far. The first say Strength.. Well duh. The 2nd say Attack Power and the 3rd say Damage. While testing I've gotten mixed results. Sometimes the weapon with Attack Power superirioty does more damage (both in sheer numbers and Recount damage done) and sometimes it will be the weapon with Damage superiority that wins. I want to be able to understand which is better so that i can actually know why I'm picking the weapon I'm using and not just going by item level like I've been recommended to do. 


To maybe help a little let's use a specific example that I'm trying to figure out currently. 


When I use this Ghostheart those stats are; Damage 14,200-19,440, DPS 4,985 and Attack Power 11,580.


When I use this Warmace of Taran Zhu those stats are; Damage 13,301-17,858, DPS 4,493, and Attack Power 13,036. 


The numbers I see/recount damage done is about the same and I'm curious how. It seems like the Warmace would be worse despite the +Strength because of the 2,000 damage difference however the Attack Power is significantly better on it. Does that matter? What do the 3 of those stats do? What do skills scale off of? Any help would be great, I really enjoy the game so far and I'm just trying to understand why I'm doing the things I'm being told that I should be doing so I can eventually make my own decisions and not follow guides or peoples advice. 


Thanks in advance for any replies and sorry for the long drawn out topic.

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As a warrior you gain attack power based on strength (1 Str = 2 AP), which is why it's your primary stat. Agility is essentially useless for you. The item level (ilvl) of the two weapons is far enough apart to the point that the sub-optimal weapon may seem to be performing equal/better but you'll always be better served using the highest ilvl 2-hand weapon with strength on it. If the ilvl is higher the weapon damage and DPS will be higher also. The choice between 2 equal ilvl weapons will be based on their secondary stats (hit/expertise and mastery/crit/haste) and which ones you prefer. Hit/expertise are both top until their caps (7.5% of each) and for arms it would be crit>mastery>haste after that. The same logic applies to armor, just without the damage/DPS part, that's only on weapons.

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Alright, so then in the case of these 2 weapons I would be better off using the Axe even though it has a lower ilvl because it has strength on it?

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Definitely. Weapon damage *is* important, never forget that, but unless the difference in ilvl between the 2 weapons is huge (speaking of ~30-40+ here) the lack of strength on the weapon won't make up for the increased damage.

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