Starcraft 2: What's the easiest order to do the missions on brutal difficulty?

Solution 1:

Well, the most obvious path would be to do Smash and Grab, and then do The Dig (Xil) as soon as it appears, because that opens up the Zeratul missions, which will allow you to fill up your Zerg and Protoss research points.

Solution 2:

For most missions, the order doesn't matter, but there are a few key units that it pays to get as soon as possible.

Vikings are useful in several missions, so I think it pays to finish the colonist storyline as soon as you can. In particular, they can be used to knock out Protoss air in "Welcome to the Jungle" (they're way better than goliaths). They're also useful for getting the research in "The Dig".

Battlecruisers can also get help get through some of the tougher missions like "Engine of Destruction", so complete "Maw of the Void" as soon as it's available.

The Zeratul missions don't benefit from any units or upgrades obtained in previous missions, so complete them as soon as possible to get the research.

Solution 3:

I personally found this very very helpful.

From TeamLiquid:

Mar Sara 1: Liberation Day -marines
Mar Sara 2: The Outlaws -medics
Mar Sara 3: Zero Hour -bunkers/turrets
Artifact 1: Smash and Grab 4protoss(4) -maurader
Colonist 1: The Evacuation 3zerg(3) -firebats
-
Covert 1: The Devil's Playground 3zerg(6) -reapers
Rebellion 1: The Great Train Robbery 3zerg(9) -diamondbacks
Rebellion 2: Cutthroat 3protoss(7) -vultures
Artifact 2: The Dig 3protoss(10) -S.Tanks
Prophecy 1: Whispers of Doom 3Zerg(12), 3protoss(13)
-
Prophecy 2: A Sinister Turn 3Zerg(15) 3protoss(16)
Prophecy 3: Echoes of the Future 4Zerg(19), 2protoss(18)
*Prophecy 4: In Utter Darkness 3 Zerg, 3 Protoss
Artifact 3: The Moebius Factor 3zerg(22) -Medivac
Colonist 3b: Haven's Fall 3protoss(21) -Viking
Artifact 4: Supernova 4protoss(25) Banshee
-
Artifact 5: Maw of the Void 4protoss -Battlecruiser
*Colonist 2: Outbreak 2zerg(24) -Hellion
*Covert 2: Welcome to the Jungle 3protoss - Goliath
*Covert 3b: Ghost of a Chance/Covert 3a: Breakout
*Rebellion 3: Engine of Destruction 3zerg - Wraith
*Rebellion 4: Media Blitz - Thor
*Rebellion 5: Piercing the Shroud 3 Zerg, 4 Protoss
-
Final 1: Gates of Hell
Final 2a: Belly of the Beast /Final 2b: Shatter the Sky
Final 3: All-In

*=option if not on a speed run. also note that if you save Haven, you have 
all research for zerg. i thought the 40,000 was more worth it since i never
use psi emitter, and if its a speed run you'll probably do nydus all-in.

Prioity Purchases: bunkers, comm centers, SCV repair, stim, medic heal, 
S.Tank, Banshee, merc tanks, merc banshee, merc vikings, 
merc battlecruiser, turrets, Viking, marauder, firebat. (in that order)