Story, Events, Exploration and Simulated Universe weeklies, are probably the best for someone that just started. Expanding Simulated Universe is also good but I feel it would take too much time for a beginner.
Once you get strong you can also get jades from endgame content like MoC, Pure Fiction and Apocalyptic Shadows.

Haven't played for a year, but I believe that Simulated Universe (SU) is the best place to go; you just need to level up to unlock most of it.

It gives Jade rewards for finding everything in it. You can run it without power and sometimes it rewards tokens (same as using trailblaze power in there) that allow you to run it with gear rewards.

I can't remember how much story you need to progress for most of the content though, sorry.