I suggest you take the court option. The officer doesn't care about whether you go to court because he is not a witness in this case (he didn't see the accident) so he can't testify at trial. This is different to the cases where the officer stops you, because on those cases by going to trial you are contesting his action. In this case, the other driver is the only witness and is the one that could testify at trial. You will need to go to court twice though, first to pretrial conference with the Judge and then to the actual hearing if you elect that option. An attorney could probably at the very least negotiate the points off your record and maybe even get the case dismissed depending on whether the other driver testifies and what he/she testifies. If you elect the school option you will have to pay the ticket and go to school. If you negotiate a plea with the Judge, you may have to pay court costs, but not the ticket or go to school. Usually the court costs are less than the ticket, so you end up better off. Some attorney give discounts to Avvo users so make some calls before choosing one. Hope this helps.
This does not create an attorney/client relationship. This does not constitue legal advice. It is limited to facts of the question. You should consult an attorney before making any decisions based on this answer.
Always fight an accident case. You are dealing with lay witnesses as opposed to police officers who know how to testify. Hiring an attorney will help in cross examining these lay witnesses. Go the court route.