(Some of the references to Operations being Level 55 or whatnot are now out of date since 4.0 changed how end-game Ops work - but the chronological order still stands.
Make sure you have the "Show Exploration Missions" option toggled On on your map screen or else there will be some missions that aren't available. If you want to see everything, here's a list of all the post-50 content in chronological order. A guide to the chronology and progression of the SWTOR storyline, including all planets, flashpoints, and operations in a visual chart. Oricon can reasonably be considered a 'core' story arc too, set between Makeb and Forged Alliances, but be aware it requires running two Operations (Dread Fortress & Dread Palace) to complete the quest line (basically, it works as a stand-alone story even if you make it your character's only involvement in the Dread War - but for full effect of that storyline you'll want to do KP, EC, SecX, TfB, S&V and the Seeker Droid mission chain first). The story quests in the game are meant to be played in a specific order, but in reality you may not come across them at the right time or might accidentally miss them all together.
If you're in a rush, the core single-players stuff is Ilum -> Makeb (Rise of the Hutt Cartel) -> Forged Alliances Flashpoints (you can select solo-mode for all of them) -> Rishi / Yavin (Shadow of Revan) -> Ziost -> Knights of the Fallen Empire -> Knights of the Eternal Throne. If you are just beginning your adventure in Star Wars: The Old Republic, you may realize that there are an incredible number of quests available in the game, and a vast range of story and lore for you to explore.