The way I prefer, at least when traveling on my own dime, is the NJ Transit #62 Bus to the PATH train...takes 45-60 minutes from EWR to lower Manhattan and costs less than $3. Time-wise, it's not that much slower than taking the much more expensive AirTrain, because at night and on weekends the NJ Transit trains don't run as frequently as the buses. There's even (limited) space for luggage on most of the #62 bus fleet.

As far as safety, the bus does go through some rough areas of Newark, but as applies in any urban area, your son will be fine as long as he acts like he knows where he's going.