GEAR
A skilled person can survive in the wilds, or in the city with only their wits and no other tools except their mind. It is really difficult and annoying to do so. Humans are a tool making species, and there are plenty of tools out there already, so you should acquire some of them, and learn how to improvise and make others. First and foremost you need something to lug your stuff around in. US military surplus backpacks and duffle bags are great, inexpensive choices. Regardless of your choice of pack, choose one that is sturdy and will hold what you need.
You need a sleeping bag. Blankets are fine, but a sleeping bag is better. Choose one rated for around 20 degrees. Keep in mind this rating does not necessarily mean “warm and toasty” at 20 degrees, but “alive and somewhat warm” at 20 degrees.
Now add a blanket to your kit. Choose wool, or a good fleece. This blanket can mean the difference between “warm and toasty” or just “alive” at low temperatures. A good blanket may also be all you need in really warm weather.
Long underwear. This speaks for itself. It also will keep you warmer in your basic sleeping bag.
Heavy socks, knit cap or “beanie” and heavy gloves. Wear these when sleeping, they will keep your extremities warmer. A scarf may also be a good choice.
Rain coat and pants. 'Nuff said.
A strong tarp. The best ones are the kind with a silver colored top and a brown bottom. Add some stout clothesline and maybe a few bungee cords. An 8' x 10' tarp will meet the needs of most individuals.
A pocketknife. Get one that locks, non locking knives, even a “genuine swiss army” type while maybe good steel, are also dangerous. Stay away from cheap knives. Generally speaking you get what you pay for. If you can acquire a decent “leatherman” style multi tool you will be ahead of the game. A knife with a semi serrated edge is useful. Get a good sharpening stone while you're at it.
Pepper spray. Self defense uses. Be aware of local laws governing the ownership/use of pepper spray or similar devices.
A basic first aid kit. This should include bandages, aspirin (or other suitable pain reliever) safety pins and disinfectant.
A basic toiletry kit, razors, comb, hand sanitizer, tissues, female hygiene if needed, and foot powder.
Flashlight and portable radio with batteries and earphones.

This is a basic kit, to be added to as the individual sees fit.