I don't know tons about New Jersey weather, but I am guessing there are a number of days each year where its raining and 35*F. Considering the lenght of your ride (it isn't short enough that you can just get wet and be fine), make sure that in addition to a coat that you have rain pants and a way to keep you feet warm and/or dry (if they are dry, they will likely stay warm). I have goretex shoes (there are a few mountain clipless shoes with goretex) and use leg gaiters between my rain pants and shoes. It works wonders on that weather.

I find that my stuff usually dries during the day. However, I have plenty of space to let my stuff dry at work, and there is good circulation. I always stuff gloves with newspaper, but otherwise just hang it on hangers (they minimize bunching together of fabric). Shoes probably won't dry if the inside gets wet.

Good luck!