Improving my gear score depends on how much gold I spend

I have a boosted toon, and I'm unsure about gearing up. I got criticized in a heroic dungeon for having a gear score of 2727, even though I ran two before that without any issues. Regular dungeons don't seem to provide upgrades. I eventually want to tackle normal ICC and the highest heroic level dungeons.

Adding more context, I've smoothly completed two heroics, but in the next few, people took issue with my gear score despite me consistently pulling 2.7k-3k DPS as a frost death knight. It's odd that Blizzard allows us to queue for heroics and even the first gamma with a fresh boosted toon.

The approach to this issue varies based on how much WoTLK Classic gold you're willing to spend. There are viable options for gear through BoE pieces and rep choices to kickstart your progress:

    Reputations: Focus on Ebon Blade for slow weapons and Sons of Hodir for shoulders, both essential for enchantments. Questlines for these reputations also yield some emblems, making them a priority. Participating in Icecrown trash farm runs can net you the Ashen Verdict rep ring, a solid choice for the expansion.

    Emblems of Heroism: Use these emblems to purchase the Mirror of Truth, which will serve you well. While Heroism emblems may not be optimal, they can still get you neck, belt, and glove (tier) pieces, useful for replacing leveling greens.

    Emblems of Triumph: Downgrade emblems to Triumph and acquire the Sigil of Awareness, a top-tier choice. Spending 160 emblems on tier 9 gloves/shoulders +2 pieces with a decent set bonus is a wise investment. Afterward, consider getting the Bloodshed Band, Crusader Orbs for crafted pieces, or rep tokens for shoulder/helm enchants.

    Emblems of Frost: These take time but are worth it. Weekly raids and dailies are a good starting point. Prioritize Tier 10 gear; shoulders are cost-effective, and you might luck out with gloves from VOA. Consider the tier chest or helm based on your weakest piece.

    Crafted / Professions: Invest in Darkmoon Card: Greatness and Spiked Titansteel Helm, both durable choices. Solid alternatives include Belt of the Titans, Battlelord's Plate Boots, Titanium Spikeguards, Titanium Razorplate, and the exceptional Hellfrozen Bonegrinders. The Ring of Scarlet Shadows is a good entry-level piece.

    BOE Drops: If you've been diligent with quests or converting emblems/honor into sellable gems, browse the AH for valuable pieces like Quel'delar, Cunning of the Shadows (from the Battered Hilt). Dungeon BOEs like Surge Needle Ring, Shawl of the Shattered Giant, and Cloak of Bloodied Waters are accessible options.

    Scourgestones: Once you can access gammas, your options expand. Upgrade your trinkets with Death's Verdict and Mjolnir Runestone, weapons with Caress of Insanity. Other noteworthy scourgestone items include The Executioner's Malice, Seal of the Betrayed King, Greaves of the 7th Legion. You can also purchase Primordial Saronite for Hellfrozen Bonegrinders.