Ziggy Stardust
Absolutely Sane
Do you think that a just society lets the quality of justice be decided by the wealth of the family?The family of the victim.
And investigating crimes are rather expensive, so I'd think there would be many who couldn't afford it at all. A murderer would be wise to pick poor targets because he'd know he would get away with it.
It sounds to me you are charmed by the principle of a society which governs itself. And I can see the charm in it. I'm very sympathetic towards it myself. But as long as people are motivated by greed and selfishness the system simple can not work in a way we would consider righteous.
The consequences of your answers aren't that complicated to determine. My advise is to go beyond just having an answer to having a practical solution. Accept that the society you have in mind is a worthy one but we as human beings have a lot of growing up to do in order to make it work.