In general, the fastest way to level up is to search out all of the NPC’s and do as many of their missions as possible. In general, they pay very good money and XP rewards and also some IP.

They will take you through all of the basic careers as well. Some of the NPC’s will not talk to you until you get more XP in a specific faction (E.g. Ashar, Wesbec, C.A.M.P. – Crafting). Work on generic missions of that type to increase your faction XP and then go back and talk to the NPC’s again until they are ready to give you a mission.

You may also find that you are blocked on a particular NPC mission chain until you get more cargo space, or more combat capability. Leave that NPC and cancel the mission and move onto another one and come back later when you have upgraded your ship. There is no penalty for canceling an NPC mission, so keep notes and record what each NPC wants and work on collecting items for multiple missions at once.