In World of Warcraft, each rack will only show helm and shoulders, once you see that, you're done with that tier. There's nothing for filling them out other than having it, as far as I can tell. Certainly looks cool. Every class has these, Demon Hunters even have one lonely stand that will eventually host Night hold.
A quick workaround would be to go transmog in to the new items to remove the window. You may have to right click the item in the transmog window and select the proper tier piece as many recent tiers have identical non-tier counterparts. One final note before getting in to detail, for the tiers where you buy them: you have to wait out the two hour refund window in order for it to finalize and appear on the rack.
Classic Classes (as not Death Knights, Monks or Demon Hunters)
The trick to getting them filled out is filling out one specific item set for each tier. For things like Tier 1 and Tier 2, you need the entire set including bracers, and it must be the original items, not the later versions that drop from Onyxia.
Tier 3 will actually be AQ, as Naxx will be represented by the Wrath revamp. For classes that have multiple specs, you must fill out one specific spec. For example paladins have three item sets for some later tiers. You would need all pieces to one spec item set, rather than Prot/Ret/Holy.
You can check your appearance tab to see the name of the tier pieces you already have as they generally have one different word. For example, Legplates/Legguards/Leggings. Wow head will tell you what name is for which piece, unless you're like me and held on to non-vendorable tier because why not.
Obviously, classes that only have one set for all specs have it easiest. In the case of Sunwell tier, you have to get the PVE pieces from Sunwell, Mount Hyjal and Black Temple in order to finish that stand. Even though the pieces it shows will be the Black Temple armor, you still need the items from the full item set.
When it comes to 10/25/Normal/Heroic raids, the armor racks are based on the lowest level tierset, so you will need to run the 10 man normal version of these raids to fill out that armor rack. (Note: this is slightly different for DKs and Monks, will be explained below in their sections!)
So let's say you are a paladin and all of your racks are empty, yet you stand there in full Judgment. You are using the non-item set helm, or you are missing the bracers. Go run Black wing Lair to finish Judgment. "But Bracket" you say "I also wear full light bringer for my holy set!" Ahh, you original mogger you.
You have the appropriate visual set, yes. But remember that Lightbringer is split up between Black Temple, Mount Hyjal and Sunwell. You need to go run Hyjal and Sunwell and make sure you buy the pve tier in the appropriate spec to finish that armor rack. "Ah ha!" You exclaim "My tank set is CLEARLY ulduar. Exlpain that, mister sewer dweller."
Well first of all it's not just a sewer, its catnips and crows. Secondly, who actually uses Ulduar 10? You're in 25. I know. You want Mimirons head. You will have to either forgo his head and run 10 until you get all the tier for Ulduar, or just have one empty rack. Same goes for ICC and remember, back then many people would get 2 set bonus from two specs. You may need to fill out one spec to finish your rack.
Lastly, ToC and ICC can both be bought for gold in northern dalaran. Just check itemset names as some are mixed and poorly sorted.
Death Knight Easymode
Death knights, for the first two tiers of Cata, you can buy them from the legacy justice quartermaster in Orgrimmar (or that smelly drizzlebreeze town in elwynn). For Dragon Soul, you don't need to go past spine if you don't want to, there's no tier there. Just make sure you're doing normal and not heroic (25 is safe to run, as there's no tier difference to 10 unlike wrath).
Monks of Pandaria
I mean really, you probably have it already but just in case, Mists normal modes for Heart of Fear and Throne of Thunder are super easy for my rogue, I'm sure your monk can handle it no problem. Siege of Orgrimmar however requires heroic, as normal mode got shifted to flex during the transition to Mythic. Thank you for pointing that one out. You may need a buddy to run Heroic siege, but the above rules still apply. One spec item set, all 5 pieces.
For everyone but Death Knights and Monks, tier stops at ICC. For death knights, tier starts at Wrath Naxx and goes to Siege of Orgrimmar. Monks are the only class that I'm not 100% sure on, but according to /u/The Gorefiend, they have 5 armor stands which would mean Heart of Fear, Throne of Thunder, Siege of Orgrimmar, Blackrock Foundery and Hellfire Citadel. Locations that I can confirm.
Rogue: Entrance to the Dalaran Underbelly Inn
Warrior: Surrounding the mini arena on the wall
Paladin: On the ledge just inside the altar room to boost your Ashbringer
Hunter: Okay I lied I have one caster, they're surrounding the altar to boost your artifact
Death Knights: Around the ledge surrounding the training dummy pit Note: They're spaced waaaay the fuck out.
Demon Hunters is the loneliest number that you'll ever do, right next to your artifact empower. Thing. Those are the only class halls I have personally unlocked and can verify, but I doubt they would leave the other six classes out of this.
Druids: from syllba - In the building with Zenkiki and the shard thing from Exodar, right by the mission board.
Shaman: from /u/geddyn - For Shaman, the armor stands are in a semi-circle behind the portal to Skywall/Vortex Pinnacle.
Mage: from /u/adoggz - location
Warlocks: from /u/timberwolf146 - Warlock's appear in the section where the 'training dummies' are. Just head to the right at the fork instead of the left, they are surrounding a candle altar.
Monks: from /u/thegorefiend - The Monk ones are a little hard to miss, but they're on the first tier of steps before you reach the temple.
Priest: from /u/Andaho - Very far end of Netherlight Temple, by the windows behind the AP sink thing.
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