This is of course subject to change based on what happens on the PTR :

Emblem of Conquest lets you buy :

T8.5 "Conqueror's" chest[58] and helm[58]
S5 "Deadly Gladiator's" armor gloves[46] legs[58] shoulder[46] helm[58] chest[58]
PvE non-set armor - amulet[19] gloves[28] belt[28] pants[39]
Runed Orb[18]
Emblem of Valor[1]

Sources of badges -
3 badges from : Violet Hold, Utgarde Keep, Azjol-Nerub
4 badges from : Halls of Lightning, Halls of Stone, Oculus, Drak'Tharon, Utgarde Pinnacle
5 badges from : Gundrak, Nexus, Old Kingdom, Culling of Stratholme w/timed run
= 49 badges per day

Naxxramas gives 16 badges, OS 4, EoE 4, Vault 4 = 28 per week [28 more if you also ran these on 25 man]
+5 for the satchel from OS available on 10 and 25.


My rule of thumb is ~15 mins per badge. So if you want to buy the full T8 level PvE items available then it will take ~60 hours dedicated to farming badges.
There's also BoE boots [belts too] available made with 6 runed orbs = 108 badges [or you could just buy them].

edit: stupid emotes