Simply do the missions that are labeled, " rank progression". Eventually they will invite you into the system. They tend to be close to SOL so going to
Wise, Altair, Alpha Centauri, and Bernard's Star is how I did it.
While I have it, the warrant detector is a separate system that you have to activate under a secondary weapon system and it is for bounties in other systems. So if you're in Federation, the guy may be clean there, but may be wanted in Empire. So I don't think you need it in SOL to have it instantly tell you if they are clean/wanted.
I recommend the sites near Wohler Station in Kremain. Wohler station is a full on station unlike Boswell being an outpost. So if your canopy was busted and you still have the basic 5 minutes of air, you don't sit there pounding the request docking button and getting denied at Boswell. Wohler you're pretty much guaranteed to have it granted and get in there to get repaired.

But once you get the permit for SOL, I am really liking the resource sites around Jupiter. The station is only 1 Ls away and there are like 5 sites around Jupiter.
Strangely enough, there are no resource extractions sites within Saturn's rings.
You can go super cruising around and look for USS's and see if there are any wanted people there. You can equip yourself with a frameshift interdictor and interdict wanted people. You can also accept contract kills as well( but they tend to be Anaconda's so have a ship that is capable of taking one out).