Here are the regulations for that area:https://www.fs.usda.gov/detail/whitemountain/learning/safety-ethics/?cid=STELPRDB5186355
Either a bear canister or hanging is allowed. Hanging is much lighter, but the only place I've seen the perfect branch to hang food is on the brochure showing you how to do it. Canisters are more foolproof but are heavy (and they seem to get heavier the farther down the trail you get.)
You mentioned some places have bear boxes available. That is a great option, but unless you have a reserved campsite (not very common in the back-country) you may not be able to count on it. If your planned trip has bear boxes at all of your planned stops, I would still bring the ability to hang food in case the bear box is full when you get to a location.
I recently bought a bear bag kit from these guys:https://liteaf.com/product/flat-bottom-bear-bag-kit-complete-bear-bag-kit/
Kind of pricey for something you can easily put together yourself, but it is extremely light and it is a complete kit with everything you need. I am happy with it.
If you decide on a canister, do note that I believe the BearVault is still not allowed in the Adirondacks due to a bear (now deceased) figuring out how to break into them and then teaching her children (
I know I am not giving you straight answers to your questions, but like lots of things in life... it depends. Give us more details perhaps we can give you a more refined solution. How many days with how many people will you be out?