This is likely The Status Civilization by Robert Sheckley (Wikipedia link)
On first arriving our hero learns of his initial status in a lecture delivered to the whole group (emphasis added):
"The first thing you new men should understand," the Quaestor said, "is
just exactly what you are. That's very important. And I'll tell you what
you are. You're peons. You're the lowest of the low. You're
statusless. There's nothing lower except mutants, and they aren't
really human. Any questions?"
The Quaestor waited. When there were no questions, he said, "I've
defined what you are. From that, we'll proceed to a basic
understanding of what everybody else on Omega is. First of all,
everybody is more important than you; but some are more important than
others. Next above you in rank is the Resident, who hardly counts for
more than any of you, and then there's the Free Citizen. He wears a gray
finger ring of status, and his clothes are black. He isn't important
either, but he's much more important than you. With luck, some of you
may become Free Citizens.
Our hero fails to take some of the advice given in that lecture, wanders abroad, gets into heap of trouble, seeks desperately for shelter and finds only the gift of handgun, gets lucky with it and kills one of his three pursuers. The other two suddenly stop their attack, put away their weapons and begin treating him with a (limited) degree of basic respect:
"All that remains for you to do," the first man said, "is to go to the
Registration Office and collect your inheritance."
"Your inheritance," the Hadji said patiently. "You're entitled to the
entire estate of your victim. In Draken's case, I'm sorry to say, it
doesn't amount to very much."
Other notable features of the society on the prison planet include drug abuse being mandatory and gladiator-like events as punishment for people who break the mores of the place (which includes our hero).
There is also a romantic sub-plot.
Eventual escape takes our hero back to Earth where he assume the role of a pollster in order to learn how the Earth works and begins seeking out both what really happened to him, and the leaders of the justice system on whom he hopes to take revenge.
There is a surprise conclusion featuring the chief of the planetary secret police and involving who accused him in the first place.
The story is available for free from Project Gutenberg, and there is a Librivox recording as well.