What time of year are you planning on making the trip? How many will be in your crew?
Sorry...the marina in AC is Kammerman's. For some reason I was thinking of Kelchner's (they make horseradish).
I'd probably look at doing a run from Cape May to Atlantic City the first day. That's your shake-down day. It's an EASY run, and it should be a nice place to stop. Good facilities, good food, and if you don't want to sleep aboard (bad weather, etc.), there are plenty of hotels right there. The next day is the trip up to Manasquan. That's a (ballpark) 50 NM trip. That's a full day, but if the weather is good it should be do-able. Spring/summer in NJ, the wind is typically out of the south (or at least has a southerly component) so you're headed in the right direction.
As I said, we did make it going "inside" at Atlantic City. Once we got under the bridge, the greenheads were God-awful. We were getting eaten alive. Deep Woods Off wasn't strong enough to kill them. We had to put on long pants, socks, shoes, and jackets. My cousin was barefoot for a moment and a fly bit him on the bottom of his foot. Once the wind picked up, the flies went away and it was much better. We entered AC as the tide was going out, which was part of the problem. We would have had more water under us if we had timed it better, but we had made good time getting to Atlantic City and decided to try to make the run to Forked River the same day, rather than splitting it into two days. A 3'9" draft might work inside if the weather is crappy and you're in a hurry, but you really need to pay careful attention to the channel markers and the water color. For your intended purposes, I'd do as others have suggested and stay outside. But, it MIGHT be do-able inside given your shallow draft. Our "air draft" is about 42'. We didn't have any problems with the bridges, but we didn't go as far as you will. You'll have to wait for the Mathis (Route 37 between Toms River and Seaside Heights) and Mantoloking bridges to open. You'll also have to contend with 2 lift bridges as you go through the canal. You should check with the bridges before you leave to make sure they are working. As I understand it, the canal can be a bit tricky; the water flows through there pretty fast. Your best bet is to time it so you pass through approaching a slack high tide.
One advantage of going "inside" is that you can bail at many points. There are several sailboat-friendly marinas on the bay.
Again, I'd still lean toward going outside. I was nervous, because that was my first time sailing in the ocean (we sailed our Catalina 25 in the bay behind Ocean City the previous year), and my "crew" had never been aboard a sailboat before. It was only my 3rd day with the boat, and we had just gotten her "back" from having some fairly major engine work done. But the ride was amazing! We had great weather and the waves were perfect (2-3' and 8-10 seconds apart). If I hadn't heard horrible things about Barnegat Bay, we would have kept going in the ocean and tucked in through Barnegat Inlet. Instead, we "chickened out" and went inside. I put that in quotes because, when experienced captains like Auspicious tell you not to use Barnegat Inlet without local knowledge, that's telling you something.
Hope this helps!