Howdy,
That's quite a loaded question lol - so much has changed in the game, I'm not sure where to start. I can cover post-50 Dailies, as that is mostly what I have experience with...I dabble in PvP and rarely do FP/Ops, so while I can touch on those topics, probably best that others do so.
50 used to stop at Ilum, Belsavis Bonus and Corellia-Black Hole. Now, you have the ROTHC expansion and 2 additional planets/daily areas beyond that.
Makeb (ROTHC) can be initiated on your ship around L48 or so; there's a cutscene, and you're directed to the planet. Makeb is a relatively regular-sized world, with a planet-wide quest, as well as dailies. IMO, I love Makeb - I farmed it for a while, and I haven't yet gotten sick of it.
Along with Makeb is the introduction of GSI dailies - they span the galaxy, but you can't get them until L52. Too much to write about them, so in that regard (and all of this, because I'm not perfect), I suggest you take a look at Dulfy.net to fill in the blanks.
Not that you need to finish Makeb first, but beyond that, there are 2 additional daily planets - CZ-198 and Oricon. Both have starter quests on the fleet, and I suggest getting them prior to going so you get extra comms, etc.
CZ is pretty easy and straight-forward...a few quests, some 2-man Flashpoints, and a weekly.
Oricon is a bit more difficult, and it adds a small planet quest. Once you're done with that, you get dailies, a weekly, and 2 Ops. Oricon, IMO, is good for comms and if you don't have decent gear, the planet quests get you started on the gear you need for HM FPs and other things. It can be tough if undergeared and there is a lot of griefing (at least, there was)...but I enjoy it.
The Comm system has changed - you have Classic (old Black Hole/Campaign), Basic, Elite, and Ultimate. I don't typically mess with Classic...Basic is good to get you your Black Market gear, Elite your Arkanian, and Ultimate is the best you can do without doing Ops for tokens and drops. Get Basics from Makeb and beyond, then the Weeklies, HM FP weeklies and Ops get you Elites/Ults. Ops give you more of each.
Some of what I said could be in error, so I apologize in advance if that's the case. But I hope this helps you get started...I can sorta answer PvP or Ops questions, but again, I don't do much of those.
Good Luck!