You don’t want tents and bedrolls and such. The worst thing that can happen to you is that you appear to be well-prepared and stocked to people that are not. This will just make you a target, and you will have to spend all your time guarding your stuff, until a big enough group beats you up, takes all your stuff, and leaves you for dead.
You don’t need stuff, what you need are skillz. These make you valuable.
Way way back, I used to be into outdoor survival and camping. I once went three weeks in the woods between high school and college.
What you will find with stuff that you buy is that most of it is made for a weekend or two and that it will not hold up under hard use.
-You need a book on edible plants and herbs and how to find them.
-You need pieces of wire from which you can make snares.
-You need a book on making snares and deadfalls
-You need a book on learning how to tan a hide.
-You need durable multi-season clothing. Patagonia makes a stand-up pant which is pretty nice.
-You need a high quality poncho.
-You need a special knife, a commercial baker’s dough or bread knife, or a butcher’s blade. To all appearances this is a very cheap looking knife. It has a plastic handle that looks like a toy. It’s very thin, very flexible steel, that holds and takes an edge. A cheap diver’s knife is also useful. You’ll also want a pocket knife, also cheap. You’ll want these to be concealable yet accessible attached to your belt or back under your clothes.
-You’ll want a pair of light work boots, wolverines are cool.
-You’ll want a pair of running shoes, old and worn.
-You’ll want an army surplus backpack with a frame. Don’t go aluminum. You want canvas and steel tubes. Old school. You’ll want a smaller backpack that will fit in the big one.
-You’ll want a big old pot with a top.
-You’ll want nylon string, twine, and light rope, needle, thread, monofilament, fishhooks.
-Many cheap army or institutional style blankets.
-A wool sweater
-A wide-brimmed hat.
-A book on survival skills and firestarting.
Now, what you need to do is practice. Get your stuff messed up so that it looks bad and undesirable. Throw out anything that breaks or that you don’t like. Everything needs to be battle-tested. You’ll need to learn how to make fire from scratch which requires a lot of practice. You’ll need to recognize small game trails, learn how to place your snares and prepare your food. You’ll need to learn how to improvise a good shelter. A well constructed lean-to can be pretty luxurious.
Divide your stuff between the two backpacks so that you can afford to lose one and still have a complete kit. When you camp, immediately hide one a distance away, in case hungry marauders intrude onto the camp to steal your food, beat you up and take your stuff.
You need to think like a homeless person. A homeless person with good stuff is a victim. What you need to do is have a survival kit that will not arouse envy or appear desirable enough to make you a target. It should be dirty, broken down, and smell so that it looks like nothing more than garbage.
When you camp build two shelters. One will be by your cooking fire, and have a blanket and some food and supplies in it. You will sleep in a hidden one a small distance away where you can observe anybody who approaches your camp. You will not linger at your main camp with the fire. Especially when you cook. When your food is ready quickly approach your camp, grab your meal and leave some by the fire.
If somebody approaches your camp, you will be able to tell a lot about them by their behavior. Do they respect your things, or steal them? Do they take your food? Act aggressive? Then you can decide if you wish to approach and make friends on your own terms, but don’t reveal your sleeping camp even then.
Now if this sounds like the apocalypse I’m preparing you for, it’s not. You want a be hobo, a person without means, this is the life you can expect.