I'm not buying the sad newbie..plea, since you are the proud new owner of a 37' sailing Vessel.....;-)
Re: weather, you're right, it's a combination of all of the above:
Wind speed, Direction, sea state etc.
By way of example.., there's a small craft advisory for the coastal waters off NJ from saturday afternoon to sunday evening. Small craft advisories are not in themself a concern for you..but in this case they're predicting S winds gusting to 25 for sunday afternoon.
seas 3- 5 feet. In your case ..heading south to cape may..this would not be what I would call a favorable report. It wouldn't nec. deter vessels with ample crew...willing to tack down the coast for 24 hours..(.it wouldn't be a fun motor sail....)
National Weather Service Marine Forecast
If I were looking to head south...I like the late monday/tues/ early wed window better..with Tues being the best..with NW winds......seas 2-4....
The nice thing about staging yourself at Sandy hook, or the Highlands is that you can stick your nose out..and see what's going on...if you don't like what you see, you can come back in at manasquan and take the inside route through Barnagat bay for a day...or sit out another day at Sandy hook...
Someone else may have a different take...but I'm assuming you'd rather not beat into a 20 to 25 knot breeze for 24 hours.. ( 25-30 apparent)