Hey Wry - we are neighbors I'm down the street, or at least Rte 252, in Media, 'everybody's home town'! Enjoy SXM and Saba, all the info you've gotten here is spot on based on my experiences. And yes - you do need a car unless you plan to stay at your resort which would just be a waste!
For local Jersey diving, you may want to check out East Coast Dive in Northfield, just outside AC - -
Welcome to EastCoast Diving. (Disclaimer - my better half does dive master stuff for them and I think a couple of their employees/volunteers lurk around SB) Anyway, they offer a dive master escort/buddy for those looking to get their feet wet in Jersey diving. Yes, diving NJ is another hidden gem of the Garden State - great diving, especially for the seafood lovers. Nothing beats fresh lobster, flounder, tautog, mussels, scallops..ok, I'm ready for lunch! They dive the Atlantus out of AC run by the Larsen brothers Brian and Andrew (Larsens Marina in Sea Isle). (Good guys, almost said kids, as I remember them gassing up my waverunner 15 years ago...Other boarders have dove them as well - see the local diving section) They also schedule trips on the Ursula (Sea Isle) and the Dina Dee. Their website lists planned dive sites (sites subject to change given the Capt and conditions) and quite a few are on the shallow side this year.
As for gear - most of the boats and shops have specific requirements. Usually the boat/shop website lists local diving requirement/equipment list. I would not venture out without a pony bottle, SBM and reel, however, if you are doing escorted or training dives, those can be overlooked. You can also rent pony, wetsuit (7 mm farmer John), dry suit, etc. I've agreed to do some local diving this summer - usually I like to sleep on Sat and Sun morning, I dive wet so lots of lead and getting back up the ladder can be a challenge as both knees are compromised from skiing injuries.
East Coast has a dive club as well. Gary Gentile (Philadelphian and Doria diver) was guest speaker at the March meeting, interesting guy.
For more local diving see Blue Horizon on Delaware Ave - did my initial training w/ them, great guys - or Adventure Scuba formerly in Plymouth Meeting, now over in Bridgeport - took Nitrox w/ them and a group trip to Bonaire, very interesting group of owners, all very nice. Adventure seems a bit more tech - deeper, planned deco, doubles plus ponies and rebreathers (even in Bonaire).
Above based on my experience only, your mileage may vary and not to say there aren't other great boats/shops around, I just haven't dealt with them. I will be up the quarry at some point late summer as hopefully my brother and nephew get their stuff together, take the course and get their cards! Hope this helps!
Lin