Welcome back to NJ! As you noticed, we have many clubs running autocross events in the area. To name a few:
NNJR (Northern New Jersey Region) SCCA @ Meadowlands
NNJR PCA (Porsche Club of America) @ Meadowlands
MSNE (Motorsports Northeast) @ Meadowland
SJR (Southern Jersey Region) SCCA @ Bader Field in Atlantic City
I'd recommend NNJR SCCA events since they are one of the most novice friendly clubs. They have loaner helmets and good instructors who can ride along with you. You can ask questions to any of the veteran autocrossers there and anyone will be happy to help you. There will be an event on May 26th. If you come, look me up. I will be in a yellow Formula Ford (CM) and should be easy to spot.
I noticed that some of the NNJR events are not listed on AutoX4U.com event page. You will find the info on their events in the following link: