To add to what Red Jacket said.
Install a clean version of Doomsday.
Install Armageddon into the Doomsday folder
Apply the 1.2 Armageddon patch into the Doomsday/Armageddon folder.
If you have the Anthology then Armageddon is a stand alone game.
Install Arma
Apply the 1.2 patch to Arma. Make sure the installer directs it to Paradox Interactive/Armageddon not Paradox Interactive/Doomsday/Armageddon