Hearthpwn

Dirty Rat, Potion of Polymorph and Snipe all help. Even Ancestor's Call in Wild would work.

Priest has a few answers for after they complete the quest, from a Pint-Size Potion and Shadow Word: Horror combo, to Dragonfire Potion and Lightbomb also in Wild.

I imagine Brawl could at least delay your death a turn or two as Warrior, and a really good control warrior deck might be able to consistently have a fair game against Quest Rouge, but I don't have a clue.

Maybe Reno-lock could stand a chance, but I doubt it. anyways, you could put as many of these tech cards I mentioned above in a deck and start a Quest Rogue resistance!

Here's a replay I just had against a Quest Rogue with a Hunter deck: https://hsreplay.net/replay/HNMP2G2rEnAN249ULNih3N

it doesn't have several legendaries mentioned in the description, and has several replacement suggestions to make the deck even cheaper. that's how.

I posted a new line in the description linking an extra budget version.

I apologize for my previous response. I have made these Changes:

-2 Doomsayer +2 Kindly Grandmother

-2 Hungry Crab +2 Secret Keeper

-2 Flare +2 Snipe

The Mage one needs to both have its cost increased and Battleground count reduce both by one. Otherwise, playing a lot of little Stealth minions would wreck the game worse than Malygos ever will.

wow you guys, Blizzard isn't putting any of these trash cards we make in the game anyways. But there is hope: just like Golakka Crawler came after Patches, so will an anti-Secret card come after Arcanologist. Just wait until the next expansion and complain about the new broken warlock cards they're going to release to make the class playable again. In the mean time, I'll take the free Mage and Priest wins XD. 

Quote from Funkdat >>

A lot of things about this deck confuse me. You run so many pirates which have effects based on have a weapon equipped and yet only run two weapons. You run Kill Command and yet you only run six beast in your main deck (two are five mana). It will rarely be live at five damage until you finish the quest and by then it might now matter. Two copies of Flare is over kill. You only never need one to stop Mage decks. If you want deck thinning, then Tracking is a much better option in this deck. It helps you search Raptors once the quest is done, making the major flaw of the quest (luck of the draw) less of a problem. And I won't even get started how counter productive it is to run Doomsayer in a aggro deck that's all about spamming the board. I've experimented with this quest a lot since I pulled the card in my first packs. You can win some games off sheer luck, but I often won without finishing the quest and most meta decks each this deck for lunch. It often just ends up being a less consistent version of Mid-range Hunter. Once you finish the quest, it's only really effective if you have Tundra Rhino, but you aren't even running Tracking to help search it. 

My example is a bit of power creep in that it is essentially the same effect but for one less mana. If you want SUPER power creep, I'd make a card like this: 4 mana 4/3 "Stealth. Secrets do not trigger."

In response to ry622:

Your argument for 0 cost cards is compelling, but in the situations with Emperor Thaurissan you're reducing the cost of more than one card, and generally the cards involved give you a shot at killing your opponent. the cards I reduced to o mana can only aid in minion removal, I'm not sure why those cards would pose an issue being 0 mana. (Charge, Savagery) Also, they don't see any play time in any deck known to me so even if they literally gave you mana I'm not sure they would be used then.

I left 'transform' effects alone because they are just as common as a nuisance and can be played around by any viable deck. If your entire deck relies on one minion not getting transformed I suggest playing a few more end-game threats in the deck, or maybe a charge minion or two.

I am going to increase Devolve Polymorph and Hex all by one mana to be 3, 5 and 4 mana respectively because they are powerful cards, but the effects don't need to be changed.

Just kidding, I'm going to put Overload: (2) on Devolve.

In response to AlchemistApprentice:

By Epic Price tag, I mean I want the card to not suck. (Unlicensed Apothecary and others)

Gadgetzan Socialite: I can see your concerns, however your points in both the effect in Arena and Earthen Ring Farseer are kinda out of place. For the tempo play to work in Arena, you have to pick a card in expectation of picking another card that you may never see, there are much worse single cards than the combo with Embrace The Shadows and Farseer is a 3/3, that's why he costs 3.

Misdirection: I must admit, the beta freeze is kinda meh, but your version of Misdirection would be ran in nearly every Hunter deck. I don't want to copy Noble Sacrifice but I feel like a similar effect should happen for Misdirection. I was thinking something like this: "Secret: Choose a friendly minion. When an enemy attacks your Hero, it attacks that minion instead."

Wow! freaking lucky!

lol, you totally stole this. . . 

http://www.hearthpwn.com/decks/814911-red-mana-miracle

Sherazin, Corpse Flower? lol

I put the Eggnappers in since they spawn little Beasts and I wouldn't argue with the Crabs Switch, but I tend to value playing a minion turn 1 rather that getting a tempo swing in only some of my matchups.

Hey man, love the deck! I don't have several of the legendaries, but I made replacements and formulated this budget deck: http://www.hearthpwn.com/decks/853629-likafosss-budget-burn-mage 

I had to link you since I mostly copied this deck, hopefully it draws more attention here!

what rank(s) are you playing at? this deck it targeted for ranks 14 and above where the 'meta' decks are more common.

Also, Doomsayer is there for just that reason. You might like to run a pair of Glacial Shards in place of the Hungry Crabs and maybe a Snipe or two for more tempo/removal.