In my case, I knew where to start the story, but purposefully avoided starting it until my fleet was close to endgame strength because I suspected they would throw high-powered enemies after mine, and the only way to beat them (without possible frustration) is to have equal or greater firepower than theirs. Some of the enemy fleets appear to be on par with 150k+ or 200k+ bounties.
If not for Ziggurat and Janus device, I would want to wait until endgame (strong enough to steamroll 250k+ bounties) to start the quest. Even then, I am still tempted to wait until endgame.
As for finding stuff, I had the most frustration in the Law and Order segment with the League's archon.