The most efficient way to commute to NYC is to get the bus in Mt Laurel, NJ. A lot will depend on what time you travel. I would advise that you Google map from your proposed Woodbury location to The Greyhound Bus Terminal on Fellowship Rd and Route 73 in Mount Laurel. The bus ride takes 1hr 40min and goes to the NYC Port Authority. Few people in Gloucester County do this but it is certainly an alternative. The bus ride is comfortable and people often work during the ride via laptop. It is the same congenial business crowd everyday. Most of them however live in Burlington and Camden counties.
There are also other alternatives like the Riverline from Camden to Trenton and then the Hamilton train or travel the NJ Turnpike to the Hamilton Train.
Your housing costs in Woodbury will be significantly lower than most more northern locations. Woodbury is within the Philadelphia metro area which is filled with a broad choice of commercial, entertainment, cultural and shopping opportunities. You can be in downtown Philly in 20 minutes.
Woodbury is an old colonial era town that is close to major routes of high speed access like the NJ Turnpike and Routes 295 and 42. The west side of Route 45 (Broad St) has attractive older homes full of charm and character. It has a modest business district and is the county seat of government. The east side between Broad and Evergreen Ave. is generally less desireable due to inconsistent property maintenance, mixed property use and more numerous rental properties, that are typically converted single family residences that include significant functional obsolesence. East beyond Evergreen Ave is an area of large early 20th Century homes and a beautiful lake and park. Good luck ,Gloucester County is a beatiful place to live with lots of colonial era history and recreational opportunities.