Welcome to BP @Andrew T.
@Joseph Scorese and @Fasil Khan hit the nail on the head with what to look for and how to evaluate rental targets in NJ. My wife and I are currently looking for our first house hack opportunity as well. We were in the same situation as you, renting in NYC but moved to Rutherford to save money on rent (and get some breathing room finally).
As someone who is originally from NJ, I'd second most of what Joseph said. NJ Transit service can be spotty, not all lines are created equal. The Bergen/Main and Morris lines are great, the PV line and Montclair/Boonton lines, not so much, although they are improving. You can get a very quick and easy idea by just looking at the PDF schedules of all the lines on NJ Transit's website.
http://www.njtransit.com/sf/sf_servlet.srv?hdnPage...
Also some of the towns close to the Lincoln Tunnel have great express bus service. So be sure to check out the bus routes as well. If you head in early then they are faster than the trains, but after 7AM the times start shooting up quickly.