There is a good possibility that the points can be avoided. Please bear in mind that if you were involved in an accident, the Prosecutor and/or Judge may seek input from the other driver (in case of personal injury) before agreeing to amend your ticket to a 0-point violation. The other driver is probably more concerned with the fact that he wants to make sure that you are deemed the responsible party (not so much by the Court as by the insurance companies). Frankly, I am a little surprised that you were issued a speeding ticket if the police officer did not witness the accident. If he did not arrive until after the accident, there was probably no speed measuring device (such as K-55 Radar) used. If you were issued the summons because the officer felt your excessive speed caused the accident, it was probably his intention to issued a summons for "careless driving." Please note, mere speed is not evidence of carelessness in the State of New Jersey. A good attorney should be able to help you. There is no set fair fee. Some attorneys represent several people in court at the same time and are able to charge a little less. When you retain such an attorney, you sacrifice the individual attention that your case may need. I strongly suggest that you retain an attorney who will be representing only your interests at the court appearance.
You were most likely cited for violating NJSA 39:4-97, "Careless Driving". Many law enforcement officers issue this type of summons when called to an accident scene, regardless of whether they witnessed the event. It is a 2 NJMVC points ticket and can result in 2 or 7 insurance eligibility points as well.
You have the right to remain silent, plead not guilty, and let the prosecutor prove the case against you at trial. You also have the right to discuss a possible resolution with the prosecutor on your own or through an attorney. The prosecutor may be willing to downgrade the summons to a non-NJMVC points offense, preferably one with a low fine.
An experience traffic attorney should be able to assist you in this matter. Such attorney will also address the issue of a civil reservation in the event of a guilty plea inasmuch as there is an allegation of at least property damage at this time. Typical lawyer's fees for these types of cases will be within a range and on a flat fee schedule.