I-95 ga to Maine tollfees and transiting new York first time

Agree with Tappanzee. We take that route a lot. You have choices at that point. You can take 684 up to 84E, which cuts out all of the Rt 95 hassles/issues through Ct. Rt 84 gets a little congested going through Hartford, depending on time of day, so avoid rush hours. Rt 84 dumps you right onto the Mass pike, over to Rt 495, then up through the Northeast corner of Mass, where it meets up with Rt 95 again heading into a short stretch in NH then into Maine.
This is not a "toll free" route, but is fairly direct.

Best of luck and Safe Travels,

Jim