I've done the NE67 (which thus includes the NH48), here's some suggestions and experiences:
*Carry your normal EDC: a black bear is likely to run away from you and you'll probably only see moose in the early morning before the throngs of hiker-tourists come out. If you see a moose and it charges, you're better off taking cover than standing your ground and attempting to get off a shot at an animal that weighs 1000+ pounds and can run up to 35mph. You're far more likely to run into 2-legged threats than agitated animals as the animals tend to become less visible once the people start taking over the trails. My three moose encounters weren't around Carrigain - one was driving up to Mt. Cabot and the other two were hearing a moose a close-yet-unseen distance away hiking to Mt. Hancock and Galehead Mountain. That being said, moose can be seen anywhere up in northern NH. They're just mostly seen further north and in the
early morning, i.e. before 7am.
Alaska Moose | What to Do When You See One
Do You Know How to Respond to a Moose Encounter? - Appalachian Mountain Club
*You can open or concealed carry pretty much anywhere you need to while hiking, with the exception mentioned by
@KBCraig. My suggestion is concealed as you run into
many "crunchy granola" types while out and about hiking. Unless legal actions are your form of amusement, I suggest against open carrying to avoid any possible confrontation or incident. I never once saw a NH Fish and Game warden actively searching in the woods or in parking lots during my many trips up north. Call it luck, call it coincidence, but at no time did I have a problem with law enforcement - town, county, state, or Federal.
*Concealed is concealed and means concealed.
*I never saw anyone open carry while hiking.
*You could bring a rifle or a shotgun however you'd be far more conspicuous and you'd be adding 6-10+lbs of unnecessary weight to your day trip pack. I'm going to be blunt here: Carrigain is an easy mountain unless you're not in good physical shape and beyond an extremely rare angry moose or bear sighting, you're probably not going to need a rifle or a shotgun with you. If you're legitimately concerned about being attacked by bears, bring bear spray in addition to your EDC. You also can't really pack out a shot moose with normal hiking gear, so try to avoid shooting one in self-defense
*You do not need a concealed carry permit in NH. NH's Constitutional Carry does not have any caveats like Maine's where you still need a carry permit for certain state parks. You don't need a non-res permit to concealed carry a pistol while hiking the Whites. Now, if this is something you're doing regularly, it might be a good idea to get a non-res permit.
*If you stick to a concealed handgun, you won't run into the issue of "hey bud, where's your hunting license?" Also, casual hiking season in the Whites ends around late September, maybe leaf-peeping season on the smaller mountains that get less snow. NH Archery Deer Season begins on 9/15, so if you do another hike between 9/13 and say Columbus Day, wearing orange is a good idea, like an orange t-shirt or hoodie. Some hikers wear bells on them to warn bears and hunters - I think it makes you seem like a beagle or a hunting dog. Dogs wear bells.
Edit for one final one:
*NH basically has no knife laws. Feel free to OC or CC a knife. I've OWB'd a hunting knife a couple times but it can get in the way.