I hiked the Appalachian Trail two years ago, making it 1400 miles from Georgia to Maine, before I was forced to stop because I got sick. My pack and all durable equipment weighed 18 lbs. and 30 - 35 lbs. with a week of food and daily water.
1. Shelter - be it a silnylon tarp, a bivy, a tarp tent, a camping hammock, or a full tent, shelter is key to protecting you from the adverse effects of the weather and environment. It should protect you from rain, wind, bugs, and somewhat from the cold.
2. Sleeping system - sleeping bags, sleeping quilts, foam mats, inflatable mats, underquilts, etc. whatever you use must keep you warm and insulate you from the ground. The ground leeches most of your heat, not the air, although most of your heat loss is from your head and face. Use a reflective closed-cell foam mat under you and wear a wool cap at night to minimize heat loss.
3. Illumination - LED flashlights, headlamps, solar lights, etc. all should be small and as lightweight as possible. Carry one extra set of fresh batteries and possible a spare bulb.
4. Firemaking - you need to be able to make a fire, especially in an emergency, and you need to be able to do so quickly. Waterproof matches, lighters, magnesium strikers, even bow drills can all produce flame - but correctly building a fire takes practice. Learn what natural materials can be used for tinder, and how to split wet wood to expose the dry wood inside. Learn to make fuzzsticks and various types of fire lays, such as the cabin, the star, and the reflector fires. Carry a good fixed blade knife - folders can often fold back on your fingers if the lock mechanism fails, as they often do.
5. Food preparation and storage - a small "messkit" of a Sierra style cup, a small aluminum pan, a collapsible silicone bowl, and a titanium Spork tool will be your best friends. You can cook over a campfire, over a Coleman canister stove, over a homemade alcohol stove, or over a collapsible steel "twig" stove to name but a few options. Storing food is best done by hanging your food in a tree, dangling at least 15 feet off the ground, at least 5 feet out from the tree and at least 5 feet below the branch it is hanging from. Learn the PCT, or Pacific Crest Trail method of hanging a food bag at night.
6. Navigation - learn to use a compass and map. Learn to use a compass and a map. Learn to use a compass and map. I must take this time to stress, if I haven't done it before, to learn to use a compass and map. Stay on marked trails. If you do get lost, seek water and then stay put. Wandering will minimize your chances of being found. If you must attempt to walk out, find a water source and follow it downstream - water always leads to people. Learn how to use distress signals - three of anything is a call for help - three fires, three blankets, three gunshots, three whistle blasts, etc.
7. Rain protection - a good rain poncho or rain jacket/pants will protect you from the elements, but if you are exerting yourself while wearing raingear it will hold in your perspiration, getting you wet from your sweat as the waterproof gear does not breathe. Stay away from cotton clothing - when cotton gets wet it loses all of its insulative ability. Cotton clothing can lead to hypothermia and therefore possible death. More deaths in nature occur from hypothermia than from any other cause. Use synthetic wicking clothing as it dries quickly, and dress in layers. Use a good "puffy" jacket that compresses into a small ball for storage.
8.Water purification - whether it is a Sawyer filter, a Lifestraw, purification tablets, bleach drops, Steripens, etc. water treatment is paramount. Learn to use whatever method you choose before you hit the trail and make sure you know how long to boil water at your elevation. Depending on the water source I would filter, treat, and boil to make sure. It was a Giardia contamination that took me off the Trail two years ago.
9. Bathroom items - you should take a lightweight plastic trowel to dig a "cathole", toilet paper, and hand sanitizer. Remember that sanitizer does not kill e. coli, and the best way to clean your hands is with soap and water and then using sanitizer. Wash your hands as long as it takes to sing Happy Birthday twice, and scrub well. A nailbrush is a great thing to have. Carry sunscreen, sunglasses, toothbrush/paste, and bug repellent with Deet or permethrins. Check yourself frequently for ticks, and carry a tick removal tool. Learn to use it. Ticks are probably the singlemost dangerous animal in the woods as there are literally millions of them in any given square mile, as opposed to a handful of bear or a few hundred snakes. Ticks carry several diseases, including Lyme and a new one that causes an acquired allergy to meat.
10. Food - dehydrated items, hard candies, granola bars, hot chocolate packets, oatmeal, Pop-Tarts, trail mix, peanut butter, Snickers bars, Ramen noodles, instant potatoes, instant soups, Mountain House camping meals, tortillas, sliced pepperoni, hard cheeses, beef jerky, cheese and crackers, gummi bears, tuna fish foil packets, potted meat, Vienna sausages, sardines, etc. are all good choices as they all have little to no water weight. Remember to pack out all your trash and do not burn it. Put all trash in a separate bag and hang it with your food bag at night.
Do not store any food in your shelter at night, or in your backpack. Try to use a Camp Triangle - camp at the top point, cook at another corner, and store your food at the other corner, with the triangle oriented into the wind so the breeze blows all cooking scents away from your camp.