Petty Theft is punishable by up to 6 months in county jail and a $1,000 fine or both but on a first offense you won't get the maximum.
Public Defenders are appointed at your first court appearance which is usually an arraignment. They cannot be appointed in advance. On a first offense, clean record, you will probably be put on probation and made to take some kind of class which will teach you what you already know: theft is not worth it.
A civil compromise works only if it has the blessing of the District Attorney. Your PD will know how to set that up if the DA is amenable.
Don't plead guilty. The opening bid in this game is a "not guilty" plea.
BTW, the fine, if any, is levied by the court. If you receive a letter from a law firm seeking to collect a civil penalty you can ignore it. These demands are never followed up on and have no effect on your criminal case.