Welcome to the Jersey Shore!
While we are now North Jersey Shore/Sandy Hook Bay folks ... we sailed Barnegat Bay for close to 14 years between 1995 and 2009.
You will love the sailing on Barnegat Bay. Virtually every non-rainy summer day brings a predictable sea breeze that kicks in between 1100 - 1200 (sometimes 1030). This provides consistent 10-15 knot thermals for 5-6 hours. The bay is protected by the barrier islands so the only seas are wind driven. It provides the best of lake sailing with the best of ocean sailing. Fall and Spring bring frontal winds as well as thermals but its still great sailing.
Barnegat inlet indeed needs to be respected. An opposing wind/tide at low tide should be avoided as that is when you will dangerously bang the bottom in troughs. Most mornings however it is safe (before the thermals kick up) and evenings tend to be okay too (when the thermals drop down). Of course a noreaster coming up the coast or a major hurricane down south can kick up the surf even though the weather may be thousands of miles away. That said, mornings tend to be docile, afternoons a bit choppy, and evenings peaceful.
You will deal with eel grass and depending upon how far south you go ... greenheads may be an issue ... but north of the Barnegat Inlet was relatively free of both on the bay side.
You will love Tices shoal where you can dink ashore and walk across to the beach (though we haven't checked since Sandy) ... the Toms River is a great visit ... and you are approximately 120 NM from Block Island which is a fantastic overnight cruise (20-24 hours depending on hull speed). Atlantic City and Cape May are reachable in a day as are Sandy Hook Bay and NY Harbor.
Good luck and welcome!!