PvE: Tionese --> Columi --> Rakata --> Black Hole/Campaign (Black Hole doesn't have set bonuses though)
PvP pre-1.2: Centurion --> Champion --> Battlemaster
PvP post-1.2: Recruit --> Battlemaster --> War Hero
For HMs and Operations it goes like this:
Recruit --> Centurion --> Tionese --> Champion --> Battlemaster --> Columi --> WarHero --> Rakata --> Campaign/BH.
Here's my recommendation. You can either use Battlemaster or Tionese gear on the easier HM flashpoints (everything except Kaon Under Seige and Lost Island) until you can get a full Columi set. Then run Operations until you can get a full rakata set with some Campaign/BH gear from stuff like the Nightmare Pilgrim. 3 Nightmare Pilgrim kills should get you at least 1 or 2 Camp/BH pieces. After you have 3/5 Rakata and 2 pieces of Campaign you are ready to take on EC HM and EV and KP Nightmare.
I myself cannot wait until Nightmare EC comes out - I'm hoping that Bioware actually makes that one a real challenge.