Chances are fairly good you would not get any jail time for this offense. Frankly, jails are over crowded and they simply don't have room for a first time, non-violent offender.
As far as your rights? You have the right to remain silent. Exercise that right and don't discuss this with anyone. If you are charged (meaning you get a court date), you will go to court and plead "not guilty." Then you will probably have the opportunity to apply for a public defender. If you get an envelope from the prosecutor's office that offers you something like a "deferred prosecution" you should take the paperwork to the public defender's office and apply for assistance. You need to fully understand the ramifications of pleading guilty to this offense.
That you will not do any jail time is the least of your worries - long term, that is. Providing false information to a police office and lying on a legal document is a crime of moral turpitude. This will have serious and potentially life long ramifications for you. You will probably NEVER be able to get a job that requires any type of security clearance or background investigation. In a he said/she said situation in court (small claims court, divorce court, etc.), your word will simply not be good enough.
It sounds like you are doing your best to cooperate fully and didn't intend to do anything improper. Unfortunately, I believe that the stolen property charge is a strict liability crime, that is, one that applies regardless of your intentions. Nevertheless, your good will can only help you.
I do think that you should plan to find an attorney. If you qualify for a public defender, they generally are quite good, although your mileage may vary based on where you live. Most public defenders have a great deal of courtroom experience and often are quite skilled. I can't pretend to give you expert legal advice, but it doesn't sound like your case is terribly complex. You shouldn't go it alone, but a solid public defender probably will be able to do right by you.
I'm sorry that you're stuck in an unfortunate position here, and I hope it works out all right. Good luck.