Given your sailing area -- and particularly if you end up venturing further north (and why wouldn't you -- Maine is fabulous sailing!) -- a wet suit, snorkling gear, and a good sharp folding knife, are useful things to have when (not if) you find yourself snagging a lobster pot line.

Highly suggest a sharp serrated knife- it cuts lobster pot line faster than a straight blade knife....spoken from experience working in cold water. 

Welcome to the club, Mike.  All of this depends on your particular location, sailing goals, and risk appetite.  For example, we don't have as many line obstructions here in the Great Lakes as you seem to have in the NE coast, so line cutters are not as popular.  I suggest going through your cruising plans and doing a bunch of what-if scenarios.  My two risk steps are (1) what will end the party / cruise and (2) when will I need outside rescue or towing.  I try to carry enough spares to avoid any outside rescue, and enough safety gear so that we're all alive and healthy if it turns south and we need to call the Coasties. If your new-to-you boat does not already have spares, I suggest engine spares from Catalina Direct so that you have at least two spare raw water impellers, fuel and oil filters, and a generator V-belt.   I'd carry one of those glove-box starter batteries to jump start if you forget to swich your batteries over and enough tools to adjust every type of fastener on the boat.  It's much easier and cheaper to order from Defender, Catalina Direct, or Amazon now than hitch a ride to the local hardware store when you're in some scenic harbor, or five miles offshore.  For sailing, I carry enough spare line to rig spare sheets or tow something.  I carry a spare anchor and 100' rode for stern anchoring or if I lose the primary.

You've covered the "water coming in" contingency with leak stopping stuff.  Consider the much more common emergency contingencies of personal injury / illness and fires.  It's much more likely that the crew will be the weak link in your sailing plans than the well-made boat.  I carry a first-aid kit, and a more extensive kit that I've put together myself.  Most ready-made first aid kits have garbage supplies and are just collections of small bandaids and aspirin tablets so they can say "150 pieces".  I suggest getting a box and making your own up - of stuff you need and know how to use for the length of time you expect to be away from professional help.  Here's a good link for what you should consider: ​https://danboater.org/travel-health-and-safety/first-aid-kits.html  If you're going sailing more than an hour or so from help, you really should read a marine or back-country first-aid book (and have it on-board) so that you know what to do with that stuff.  Think about these things before you slice your toe open on something and you need to figure out how to stop the bleeding.  For fire, I'd consider the USCG requirements a bare minimum. If you can't control an on-board fire, your only alternative is to swim.  I don't know how cold you water is, but we would not last long in May. The most common fire will be the galley stove or grill getting out-of-hand, so we carry a fire blanket to douse those.  For thinking about scenarios, I'd look up the excellent articles by Mario Vittone (ex-CG) on safety at sea: https://www.soundingsonline.com/voices/lifelines-safety-and-rescue-at-sea 

For real emergencies, we have the required flares and the ships VHF.  We also carry GPS-based personal locator beacons (the poor man's EPIRB).  Other than day-sailing in our local bay, we always file a float-plan with someone who'll call the coasties if we're overdue.  We've got some remote areas here, and it's nice to know that you won't be stuck in some bay for a month before they look for you.

Don't mean to scare you with any of this, but you  asked what I carry.  Your family will be much safer and comfortable if you've thought about this before leaving the dock.

IMHO it just depends so much on what kind of a voyage you are on. If I am sailing locally here in San Francisco Bay, I don't need much. Handy plugs, definitely divers mask and serrated knife aboard. Our small bag with flares, mirrors, smoke, etc is always in easy reach in the little compartment under the starboard side aft cabin mattress. But no real doomsday bag. Even if the mast came down, the cell phone works just fine. My dinghy is always inflated on the foredeck, so worst case, it can be used, like to carry a kedging anchor out, that kind of thing. 

Coastal cruising out here requires a bit more, again depending on how far from civilization I am going to be. In the event that the boat was actually sinking after all attempts to plug holes (maybe a whale strike?), the dinghy is my liferaft. If there was time, I'd throw the dinghy motor on it as well. The dinghy with motor can be strapped to the side of the boat and used as an auxilliary in some situations.

On our actual out of sight of land crossings/passages, we did keep a true ditch bag, which included basically liquids, easy food items, our waterproof handheld VHF, a vast assortment of current and expired flares/smoke bombs etc., survival blankets, an extra knife, first aid kit, passports, wallets, strobe lights, an epirb, and any number of bright LED flashlights. I'm probably forgetting something, but again, for me, it just depends so much on what kinds of situations you can possibly encounter. 

Al

Seriously.  No one packed Rum?

:-D

It was mentioned above but I highly second the  recommended  handheld , water proof VHF that floats with GPS built in. Register this thru BoatUS and get a DSC MMSI number. At the same time make sure you register your on-board VHF radio or change the pior owners information to yours if they registered the radio themselves.

If your not familiar with DSC, do a quick Google search... it allows you to send out a Mayday call by holding a button for a fwe seconds and then it automatically continues to send it out. The hand held I metioned would allow you to do the same if you lost electric power in your boat or if you were in a life raft, dinghy or the water if you were in really bad straights. The Coast Guard HIGHLY recommends DSC in all their info on it.

Just a heads up on the offshore risks of holing the boat, while a whale strike is unlikely given that we're quickly eliminating the last of them, there are more and more containers out there filled with floating material just below the surface.  Hit the corner of one at speed and you're likely to have an irrepairable hole.  Perhaps low odds, but years ago an English round-the-worlder spent years prepping only to lose the vessel shortly after departing due to an invisible container strike in the English Channel.

"In the 2014 survey, WSC received reports from carriers on losses during 2011, 2012 and 2013. From those results, WSC estimated that there were approximately 733 containers lost at sea on average for each of these three years, not counting catastrophic events. When one includes catastrophic losses (as defined above) during these years, the average annual loss for the period was approximately 2,683 containers."