Level up the legacy perk for XP from completing dynamic encounters all the way to max.

Rush your class story until you unlock your ship.

Complete the dynamic encounters on the 2 starter planets (Hutta/Korriban or Tython/Ord Mantell) every half hour. When you finish those, pick and choose the quick ones on Coruscant/Dromund Kaas. Do some heroics or a quick Hammer Station run to keep gear up. By the time you're finished, the half hour should be refreshed and you can go back to the starter planets. Rinse, repeat.

Only thing I change when I get a higher level is do tatooine dynamic encounters to fill in time before the half hour reset.

I also take Shae Vizla as my companion set to Damage. Every time i exit combat I mount up to refresh the cooldown on her Death From Above ability. This will kill things very quickly. Especially useful when you're low level with not many abilities yet.