Go to both starting worlds before heading to the capital.
Get the datacrons on both starter worlds.
Explore the entire map on both starter worlds.
Get the codex entries (that aren't bugged) on both starter worlds.
I was level 10 before leaving my first world on each toon, picking an advanced class and going back to finish it, and was 12 by the time I left the second and hit the capital. This was on all 8 toons.
Don't skip mobs until they stop giving XP. Track down every mission. Always satisfy the bonus conditions for every mission. Solo the Heroic 2+ missions. Solo the Heroic and Area 4s where possible. Some are so balls hard as not to be worth the effort. Make sure you're fighting above your weight class on the first two worlds so you're getting max XP for mobs and missions.
From the capital planet on, if you follow this pattern, you will have great difficulty NOT graying out (over-leveling by more than 6) your story missions.
This is without playing a single space mission until 50 and only randomly bothering with flashpoints.
The game throws so much XP at you that wasting credits/money on the legacy XP perks is for noobs, even with the F2P XP nerf.
Don't get me wrong, the inane, draconian restrictions on F2P suck the big one, but the game is so simple once you understand what your class can do and how you can use each to break the game, especially the story missions, it only becomes a matter of how much time you want to invest to experience the story.
Both starting worlds? I start out on Tython, and can't go anywhere until I've completed the story mission there. Once that's done, I can either stay on the Republic Fleet or go to Coruscant.
The key to taking out elite mobs: your interrupt ability. Learn to stop the elite's big attack and everything becomes easy sauce.
I do. So far I've managed to kill each mission boss without much difficulty. I just finished the "Shadows" mission where I had to kill Lars Baddeg. I did that as a level 11, though I barely managed to win.
By the way, I try not to, but I think I really hate Qyzen Fess. It never fails when I'm trying to sneak through a high level mob area, he'll just flail right on over to them and start attacking, and it's at that point I know I'm fucked, and will have to go back to the nearest med center.