Although this is based of patterning results, The campaigns will begin with the zerg, then the protoss, and finally, A terran victory (SC- T,Z,P------BW- P,T,Z-------SC2- Z,P,T)
Blizzard stated that the CORE of the Xel'Naga were wiped out, so that leads us to beleive that the Xel'Naga still exist. Based off what brutetal just said, I would assume that it would be the protoss searching for the artifacts. As I have already posted, the Terran campaign will consist of an RPG/Strategy Implementation. Players will assume the role of Jim Raynor, aboard Capital Ship - Hyperion. He is accompanied by his friend, another marine, and a crew. The player may select from an on-board computer which destination to go to. In this way, the campaign may have multiple endings, or just be a twist for some fun for us.
The Protoss campaign, although not released yet, I beleive will be to aiding thier creators, and helping Artanis rebuild Shakuras. If the artifacts thing is true, then Players may assume the role of Artanis, in search of the artifacts. One problem with this though is that Blizzard stated that they will try to make every campaign different, with different play styles and such...
As of the Zerg campaign, it is extremeely unclear because the Zerg race has not been completely developed yet. I would guess that the Zerg learn of these rare artifacts, and attempt to war against the Terran and Protoss for it. And because of the new units, This would implement brand new strategies!
In the end, I would guess that the Xel'Naga extinguish all life in the Korplu Sector, because they screwed it up real bad...
None.