Starcraft 2's single player campaign missions are not done in a linear fashion, instead the game evolves from completing previous missions and you will have different mission options to pick from as you progress. Sometimes it is important to pick the right missions in a specific order so that the game is easy to beat on hard and brutal difficulty. You can get a good order of missions from Joana's Starcraft 2 brutal campaign missions guide. Although you will need to become a member of his site in order to view his brutal difficulty videos (which are done rather awesome by the way).
There is a total of 29 missions in Starcraft 2, but you only need to complete 26 of them to beat the game. The game's story is separated into different chapters, including: Mar Sara, Colonists, Artifact, Covert, Rebellion, Prophecy, and the final missions in Char.
Every mission has three achievements that you can gain. The first achievement of each mission is always the name of the mission and involves beating all the main objectives and bonus objectives. And the other two achievements in each mission are random feats of something they want you to accomplish.
As you play through the campaign, sometimes you will be given a choice to either go with mission "a" or mission "b" (it's either one or the other), these will affect the story line slightly but not drastically. An example of this is when you have to chose between going with Tosh for the Breakout mission or helping Nova with the Ghost of a Chance mission. You can always play the skipped missions through the mission log (from the bridge).
Here is a list of missions and when they can become available, and what you get for doing them:
The Raynor missions are the first three in the game. Credits may not be used until after Zero Hour.
The Hanson missions can be started after completing the Mar Sara missions.
The Tychus missions can be started after completing the Mar Sara missions.
The Tosh missions can be started after completing a total of 4 missions.
The Horner missions can be started after completing a total of 6 missions.
The Zeratul missions can be started after completing The Dig.
These missions are played as the Protoss. The playerís normally available Terran units, mercenaries, armory upgrades, or research do not matter in these missions. Completing these missions early is useful for a large boost to research, possibly making subsequent Terran missions slightly easier to complete in Hard/Brutal difficulties.
The Final missions can be started after completing Maw of the Void.
Caution: Once the player has finished Gates of Hell, unplayed missions on the Star Map will no longer be available. However, missions which have been previously completed will still be available to replay.
General Starcraft 2 Guides