Playing HOMM 3 complete and have a choice between Shadow of Death, Restoration of Erathia, and Armageddon's Blade. This noob would like to know the correct order to play them. Thanks

They were released in this order:

Restoration of Erathia -> Armageddon's blade -> Shadow of Death

While klaymen covered the order in which they were released there are a few other things that should also be noted. In terms of chronology Shadow of Death takes place before the other two campaigns, even though it was released last. This probably shouldn't have any influence on the order in which they're played however. Difficulty is a more significant consideration- Restoration of Erathia is the easiest of the campaigns, so is a logical starting point. However, Shadow of Death is the next step up in terms of difficulty, while the Armageddon's Blade campaigns are by far the most difficult, so you may want to hold off on those until you feel quite comfortable with the game.