A conviction for uninsured operation (a criminal charge) carries a maximum penalty of not more than 1 year in the House of Corrections and/or a fine of not less than $500 to not more than $1000, plus a license suspension of 60 days (plus the RMV reinstatement fee that must be paid to get your license back). Unregistered motor vehicle is a civil motor vehicle infraction (CMVI) that carries a $100 fine for a first-offense and does not carry a possibility of jail time.
If you are arraigned on the criminal charge, it will appear on your Board of Probation record (aka a BOP of CORI), regardless of how the charge is ultimately resolved. You should bring proof to your court date that you have since insured and registered your car. An attorney can also help in disposing of this matter prior to any arraignment, so that the charge does not appear on your record. Given your non-citizen status, maintaining your clean criminal record would be helpful in future immigration situations.
Please feel free to contact my office with any questions you may have.
Best of luck,