By request, I've put together a sample pre-raid gear set.

This is the Horde set. The Alliance badge gear is equivalent but has slightly different names.

This set is entirely composed of items that you can purchase with Emblem of Triumph, drops from 5-man dungeons, and one crafted item:

245 - head -

[Headplate of the Honorbound] - 75 Emblem of Triumph

232 - neck -

[Fossilized Ammonite Choker] - drop Halls of Reflection (H)

245 - shoulder -

[Shoulderguards of Enduring Order] - 45 Emblem of Triumph

213 - back -

[Platinum Mesh Cloak] - 25 Emblem of Valor (downgrade triumph badges)

232 - chest -

[Liadrin's Breastplate of Conquest] - 50 Emblem of Triumph

245 - wrist -

[Saronite Swordbreakers] - crafted

232 - hands -

[Liadrin's Handguards of Conquest] - 30 Emblem of Triumph

226 - waist -

[Shieldwarder Girdle] - 28 Emblem of Conquest (downgrade triumph badges)

232 - legs -

[Liadrin's Legguards of Conquest] - 50 Emblem of Triumph

232 - feet -

[Black Spire Sabatons] - drop Forge of Souls (H)

245 - ring1 -

[Clutch of Fortification] - 35 Emblem of Triumph

219 - ring2 -

[Mark of the Relentless] - drop Trial of the Champion (H)

245 - trinket1 -

[Glyph of Indomitability] - 50 Emblem of Triumph

232 - trinket2 -

[Ick's Rotting Thumb] - drop Pit of Saron (H)

245 - libram -

[Libram of Defiance] - 25 Emblem of Triumph

219 - shield -

[Splintered Door of the Citadel] - drop Halls of Reflection (N)

232 - weapon -

[Rimefang's Claw] - drop Pit of Saron (H)

Number of Emblem of Triumph required: 413

Number of drops: 6

Number of crafted items: 1

Gearscore: 4962

You get 6 Emblem of Frost from completing the quest chain for the three new instances, 2 Emblem of Frost for the first random heroic of every day, and 5 Emblem of Frost for the weekly raid quest. So in a little over 2 weeks, you can have enough badges to purchase the cloak (50). I you save them for 3 weeks, you will have enough for the trinket or belt (60).

If you purchase the Frost badge cloak, and splurge on the crafted Primordial Saronite boots, this is what the set looks like:

245 - head -

[Headplate of the Honorbound] - 75 Emblem of Triumph

232 - neck -

[Fossilized Ammonite Choker] - drop Halls of Reflection (H)

245 - shoulder -

[Shoulderguards of Enduring Order] - 45 Emblem of Triumph

264 - back -

[Sentinel's Winter Cloak] - 50 Emblem of Frost

232 - chest -

[Liadrin's Breastplate of Conquest] - 50 Emblem of Triumph

245 - wrist -

[Saronite Swordbreakers] - crafted

232 - hands -

[Liadrin's Handguards of Conquest] - 30 Emblem of Triumph

226 - waist -

[Shieldwarder Girdle] - 28 Emblem of Conquest (downgrade triumph badges)

232 - legs -

[Liadrin's Legguards of Conquest] - 50 Emblem of Triumph

264 - feet -

[Boots of Kingly Upheaval] - crafted

245 - ring1 -

[Clutch of Fortification] - 35 Emblem of Triumph

219 - ring2 -

[Mark of the Relentless] - drop Trial of the Champion (H)

245 - trinket1 -

[Glyph of Indomitability] - 50 Emblem of Triumph

232 - trinket2 -

[Ick's Rotting Thumb] - drop Pit of Saron (H)

245 - libram -

[Libram of Defiance] - 25 Emblem of Triumph

219 - shield -

[Splintered Door of the Citadel] - drop Halls of Reflection (N)

232 - weapon -

[Rimefang's Claw] - drop Pit of Saron (H)

Number of Emblem of Triumph required: 388

Number of Emblem of Frost required: 50

Number of drops: 5

Number of crafted items: 2

Gearscore: 5114

By request, here's the above set with the crafted pants too. If you have more money than time, then get all three crafted items to save yourself some time farming badges...

245 - head -

[Headplate of the Honorbound] - 75 Emblem of Triumph

232 - neck -

[Fossilized Ammonite Choker] - drop Halls of Reflection (H)

245 - shoulder -

[Shoulderguards of Enduring Order] - 45 Emblem of Triumph

264 - back -

[Sentinel's Winter Cloak] - 50 Emblem of Frost

232 - chest -

[Liadrin's Breastplate of Conquest] - 50 Emblem of Triumph

245 - wrist -

[Saronite Swordbreakers] - crafted

232 - hands -

[Liadrin's Handguards of Conquest] - 30 Emblem of Triumph

226 - waist -

[Shieldwarder Girdle] - 28 Emblem of Conquest (downgrade triumph badges)

264 - legs -

[Pillars of Might] - crafted

264 - feet -

[Boots of Kingly Upheaval] - crafted

245 - ring1 -

[Clutch of Fortification] - 35 Emblem of Triumph

219 - ring2 -

[Mark of the Relentless] - drop Trial of the Champion (H)

245 - trinket1 -

[Glyph of Indomitability] - 50 Emblem of Triumph

232 - trinket2 -

[Ick's Rotting Thumb] - drop Pit of Saron (H)

245 - libram -

[Libram of Defiance] - 25 Emblem of Triumph

219 - shield -

[Splintered Door of the Citadel] - drop Halls of Reflection (N)

232 - weapon -

[Rimefang's Claw] - drop Pit of Saron (H)

Number of Emblem of Triumph required: 338

Number of Emblem of Frost required: 50

Number of drops: 5

Number of crafted items: 3

Gearscore: 5206