Windows 8.1 Update 1 actually consists of multiple packages that must be installed in a specific order when installing manually. When Windows 8.1. Update 1 releases to the public on April 8, 2014 through Windows Update, the installation will be much smoother. To install it manually today the order is as follows:

  1. KB2919442*
  2. KB2919355
  3. KB2932046
  4. KB2937592
  5. KB2938439
  6. KB2949621

* KB2919442 was released as part of March 2014's Patch Tuesday and may already exist on managed computers.

Also note, that even though multiple packages will be provided, Windows 8.1 Update 1 will only show as a single entry (KB2919355) in Programs and Features.

Incidentally, the string of updates is applicable for Windows 8.1, Windows Server 2012 R2, Windows RT 8.1.

P.S. Each package will require a separate reboot. Sad, but true.

Once the update hits on April 8, 2014, the package will be much kinder than the manuall installation.  Microsoft has provided guidance for and clarification in Windows 8.1 Update: The IT Pro Perspective