Hooray! Welcome to the wonderful world of backpacking! This post is LONG, so I've made a summary list to get you started, and what follows below is a probably way too comprehensive explanation of the items. Sorry for the tl;dr!
- Backpack (with detachable day pack or separate, if needed)
- Tent (or hammock, bivy, etc.)
- Stakes and guylines
- Tarp/tent footprint
- Tent repair kit
- Sleeping mat
- Pillow or rolled-up clothes
- Sleeping bag with compression sack
- Lighter with fluid/striker
- Contained fuel and stove
- Stirring/serving utensil
- Eating utensil
- Biodegradable dish soap
- Water bottles
- Water bladder
- Water purification system
- Food (breakfasts, lunches, snacks, and dinners -- plus a bit extra)
- Trash bag
- Food bag
- Bear supplies (spray, canister, bell), if needed
- Toilet paper
- Headlamp/lantern/flashlight with extra batteries
- Clothes (shirts, pants, hat, underwear, socks, jacket, hiking boots)
- Compass and map
- First aid kit and emergency blanket
- Bug spray
- Multitool or knife
- Camera and/or phone
- Camp Towel
There are two basic types: external frame and internal frame. Externals are not as in vogue these days, although they manage awkward loads better, always maintain their shape and provide better air ventilation. Internal frames are easier to find and are reasonably adjustable.
All backpacks come in a variety of sizes (measured by liters), so you'll want to select one that fits your needs. For the length of trip you're talking about, you'll probably want to stick with one that's 50-60 liters.
If you have an REI or another outdoor goods store nearby, take an afternoon to hang out with the sales representative and try on lots and lots of packs. They're a bit like shoes--even though they all work, not all of them are comfortable, especially when you fill them with sandbags and walk around the store for a few minutes. Don't be shy about letting the sales person fit the bag to your frame and show you how to adjust it, yourself. The last thing you want on a multi-day trip is a bag that pinches your collarbone or rubs your lower back.
You may want to get a pack with a detachable daypack, or bring a separate daypack if you are staying at the same site for at least two consecutive nights. This way you wont' have to bring your entire pack with you.
You can avoid the cost of a backpack cover by using your tent's tarp or rain fly. It's ill-fitting, but you've already bought it.
There are more options here than you can imagine, but what's most important is that your tent fits the number of people you're looking to travel with and that it's in good shape. Before you buy, you may want to poke around inside a tent if the store will let you. You'll quickly discover that, even though tents come in sizes of 2-person, 3-person, 4-person, etc., "people" are evidently pretty small. I'm 5'4," and a 2-person tent fits me and my stuff comfortably, but when my husband and I use it together (and we're both average-sized people), our little dog has to sleep on our legs because there's no floor space left. Even though it adds weight, my personal preference is to go up one size from the number of people who will be sleeping in it.
The other thing to look out for is how many seasons the tent is. Generally a 3-season should be just fine for the spring-fall range you're looking at (this means everything but cold winters; down in southeast Texas where I live, I can use my 3-season tent year-round).
If I'm sharing the tent with anyone, I tend to go for models with at least two doors (it's never fun crawling over a sleeping friend in the middle of the night if you have to go to the bathroom), adequate ventilation (good for airflow, reducing condensation, and stargazing!), and a rain fly (in case, you know, it rains).
Important accessories include stakes and guylines so your tent doesn't move around or blow away, a tarp so the tent's floor is protected, and a tent repair kit in case you break a pole. Manufactures will try to sell you a tent footprint, but they're basically just pricey tarps.
A tent is not absolutely necessary. You may be fine with just a hammock and a tarp (and you might want a mosquito net depending on the creepy crawlies in your area), or you might even want to sleep under the stars. There are also one-person tents and bivouacs if you're going solo (which I wouldn't recommend your first time backpacking just for safety's sake).
A slightly off-topic bit of advice: always set up your tent in your back yard or living room before you take it camping for the first time so you know how to do it and ensure it's intact. It's never fun setting up a tent for the first time in the dark or pouring rain. Always pitch it in as level and rock-free a spot as possible, and if there's a slight incline, point your feet downward.
Sleeping Pad and Pillow
You can find some very nice, pricey sleeping pads at sporting goods stores. I bought a $5 foam roll-up mat from Walmart and have been using it for over a decade. You can also find a variety of pillows, including blow-up and miniature versions of what you find on your bed at home. If you're really trying to save on weight, you can skip this and just use some rolled up clothes inside a pillowcase. It's definitely not as comfy, but it just depends on your priorities.
These are rated to different degrees, which basically tell you how cold the temperature can get and the bag still keep you safe (not necessarily warm). You can get the rectangular variety you probably used for sleepovers as a kid, or a mummy bag, which is great for keeping you warm. Again, down here in Texas, I have friends who just use a sheet or a simple sleeping bag liner and skip the sleeping bag altogether.
If you use a sleeping bag you'll probably want a compression sack, and I suggest a waterproof one. There's nothing more miserable than a cold, wet sleeping bag.
At the very least, you're looking at needing a pot or pan. If you live in an area where you can have open fire, bring some tinder and a lighter with fluid or fire striker, but you don't necessarily need more than that depending on the food you've brought.
If you can't or don't want to cook over a fire, I recommend using a camp stove that burns contained fuel like propane or isobutane. You'll need to get the fuel type appropriate for your camp stove. Bring adequate fuel to get you through your trip (one container should be plenty assuming you don't have a huge camping party), a lighter/striker, and a pot or pan. You may also want a stirring/serving utensil.
You may also want to bring a kettle or a pot with a lid to boil water, which is often added to camp food. You'll want a plate or bowl for every person as well as an eating utensil. I rather like titanium utensils, as they're lightweight and sturdy. You may want to just drink water, but if you want coffee, tea, or another drink, you'll want to bring a mug/cup.
Bring a bottle of biodegradable dish soap. It doubles for your body, as well.
You definitely need several water bottles, and possibly also a water bladder. These things generally hold 2-3 liters of water, and they're total lifesavers, as they let you drink without having to stop walking. I can usually go through nearly a full 3-liter bladder in a long day hike, although I probably drink more than the average person. I also like to have at least one water bottle on hand so I'm not dragging my water bladder around the campfire or to dinner. So--moral of the story is bring enough containers to hold a full day's water supply. Assume at LEAST a gallon a person a day.
If you're somewhere where there is plenty of water, bring either tablets, a pump or some other kind of purification system. Do not drink water without purifying it first, period.
If you're not somewhere where there is plenty of water, sorry but you'll have to carry it all in. The good news is the trip gets lighter as you go.
It's essential that you plan out your meals ahead of time. Know exactly what you're having for breakfast, lunch, snack, and dinner every day, and make sure that you have the "extras" you might not think about, like water or spices. It's always best practice to bring at least one extra meal just in case. If you're going for low weight, you'll want to use dehydrated or just-add-water foods, as water content in food adds a lot of weight.
Bags and Food Safety
You'll need a trash bag for food and other waste you may produce. Always abide by leave no trace policies and pack out everything you take in with you. You'll also need a bag to put food and other smelly items (like toothpaste) in at night, along with rope to suspend it from a tree. This will keep animals out of your food and trash while you sleep. Make sure you read guidelines on how to hang your bag, depending on the wildlife in your area. If you're in bear country, you'll need a bear canister, which is heavier-duty than a bag. You'll also want to bring bear spray with you and may also want to consider wearing a bear bell to warn animals you're coming.
Trowel and Toilet Paper
Bring a trowel for when you have to do #2. They make all kinds of special, lightweight, folding, and otherwise backpacking-appropriate shovels that do the job. Some hardcore folks go without toilet paper, but I don't feel like it adds enough weight to be worth the sacrifice. Just bring enough squares in a little sandwich-sized ziploc.
Map and Compass
These are no-brainers! Bring them!
Good for calling for help, don't go on the trail without some way to get attention if you need it.
Flashlight, Headlamp, and/or Lantern with Extra Batteries
You'll need a source of light at nighttime. If you're going for minimalism, I'd recommend just bringing a headlamp, and going for one that has a red light option so it doesn't ruin your night vision. Whatever you bring, bring one set of extra batteries!
How much is up to you, but I usually bring fresh underwear for each day. Even though they're not exactly the height of fashion, I enjoy zip-off pants so I can change them into shorts if I get hot, and camping shirts tops with a collar and long sleeves that I can roll up. You can get all kinds of fancy sun- and bug- avoiding add-ons with these. Depending on the time of year you go, you may also need a jacket.
Bring a hat. Whether it's cold or hot, sunny or rainy, it's never a bad idea to have this, or at least a bandana.
You'll definitely want thick socks that protect your feet from rubbing. I like woolen socks because they wick moisture.
Bring your best hiking boots. You'll feel soreness in your feet more than you will after hiking all day because of the extra weight on your back.
I generally don't bring any extra clothes to sleep in, but you may want to bring an extra t-shirt or whatever is comfortable.
What you bring is up to you. A lot of what are usually the "basics" for me go by the wayside here, but I always bring at least a toothbrush, toothpaste, and deodorant. I keep a more comprehensive set of toiletries along with a change of clothes in the car for when I get back to it. :)
First Aid Kit and Emergency Blanket
Just in case something goes awry, make sure you have the supplies you'll need. The basics change depending on where you are (like a snake venom kit), but you'll at least want some bandages, antiseptic, and painkiller.
Sunscreen and Bug Spray
Keep yourself safe from sunburn and nasty bug bites. Be green with these products if possible.
Go for a polarized, UV-protectant variety.
Multitool or Knife
I'm probably an odd one, because I've been backpacking and camping more times than I can remember and I've hardly ever needed my knife, but I always bring it just in case. It's an indispensable tool.
If it's your first backpacking experience, document it so you can remember it fondly later! I suggest bringing a plastic bag so your device stays dry--just in case!
I'd recommend getting at least a small camp towel for drying off after a swim, washing hands, or washing dishes. They're very absorbent, even though they're thin.
Note: good equipment purchased new can get very expensive, so don't be afraid to check out Craigslist or go to REI garage sales--or to borrow from friends. This is how I figured out which camping stove I DIDN'T want: I used a friend's, and it didn't work! Also, if you do purchase from REI, know that if you're not satisfied with your product, you can return it at any time, even after using it, for a refund and no questions asked. Sorry to hype REI so much, but they really do have excellent customer service despite their not-so-rock-bottom prices.