What's the name of your book? I'd be interested in it, since I'm in Utah also.Google "Hiking 10 essentials"
1. Whistle
2. Water (liter per hour ish)
3. Extra food
4. Head lamp
5. compass/maps--depends on the trail
6. First aid kit
7. Rain gear--jacket and pants
8. Pocket knife
9.Water purification tablets (if you ever run out of water, you need these)
the other stuff might be overkill for short trails. But for me--anytime I am hiking in the mountains here, I have those 10 essentials plus an "emergency/space blanket". We have so many people who go out for short hikes and get lost and are TOTALLY unprepared. They get rescued but it sucks to be stuck on the mountain over night!!
Start with trail running shoes and you can move up to hiking shoes if you need to. You don't need boots until you carry a backpack or do high altitude scrambling. I use trekking poles for backpacking but not for hiking. I use an Osprey daypack because it is roomy and has a spot for a water bladder. You will drink more water if you carry a bladder. Any clothes will do. Clothing that wicks is best. And if you have issues with ticks where you are going, then you want long pants and shirts. Check out the REI Sahara shorts. (I think you have EMS out there too)
Do NOT count on your cell phone having a signal!!! Tell people your plans so they know where you are. If you are really into some more remote terrain, then look into getting a Spot It or other locator. Way better than waiting for dogs to find you:-) And that cougar video-if the guy had not been filming her cubs, that whole thing would have been a LOT less intense. She just wanted him out of there. If she wanted him dead, he would be. But you are in New York--so you need to know bears and snakes. And ticks and mosquitos. Do you have moose? They can be really scary--we have lots of them in the mountains here. I hiked/backpacked alot in Connecticut, Pennsylvania, and Virginia and saw black bears who I just managed to stay far away from/skirt around.
Go to your local outdoor store to find out if they have info nights for "Beginning Hiking". Find a guidebook on local trails. I have a guide book to all the trails in the mountains near me. It is my best friend! That way you can research trails and find out what you would like to hike. All Trails is nice but I like a guide book. Check out local hiking groups. We have several. There is a Facebook Group called "Women Who Hike" and you can join your local chapter. I am not doing any group hikes now, but it is nice to know that people are out there and I can ask questions.
And HAVE FUN!! there is nothing I love more than being out on a trail--even if it is just the trails in the foothills near my house. I just love it!