Rambling and random, pick out what you might need at the time. A lot of this involves stuff for camping, which is a great kit to have on-hand for emergencies (power outages for days and bug-outs if there are forest fires/tsunamis/hurricanes/earthquakes).
Clothing: the US Army used to do it right. What you're wearing plus: 2 pair socks, 2 pair underpants, 2 pair shirts, 1 pair pants. There's your basic, you're going to wash things every day or two. Try to look ordinary rather than a complete mess/slob/tramp. Have a spare pair of shoes in case yours get wet. One or two towels.
Insulation: multiple layers of clothing. (Not all cotton - if that gets wet your insulation is gone. Try newspapers/cardboard to cut wind. Plastic poncho for wet, you do need somewhere to sleep that's dry and non-windy.)
Sleeping in the car: warm jacket (that you can roll up into a pillow), sleeping bag (it's just a bag - you don't have to sleep on the ground with it), don't leave the windows down when there's mosquitoes around. Not recommended if there's snow, though you can manage with a really good sleeping bag and light snow.
Food from supermarkets: like restaurants, supermarkets are better for dumpster-diving (fruit and vegetables). Some students in NZ did this as part of a study, it ended up in the local newspapers. The food is still fresh enough for that day.
Camping shelter: a 3-man dome tent is cheap and roomy, a bivy bag is lightweight and more cosy. Practice with it occasionally beforehand. Remember that mosquitoes *will* get through any netting.
Skin protection: sunburn sucks. Insect bites suck. Flies getting into everything sucks. Get a combination sunscreen and insect repellent if you can. Lightweight floppy hat with a full brim.
Libraries: great for warmth in winter, cool in summer. Daytime only of course.
Extra food/survivalist stuff: depends how you want to go. It's worth looking in the library for various books on native food (you don't have to check the book out, just read it and go looking). (YMMV, I live in quasi-rural NZ - can drive 15 minutes and be in the bush/native forest.) If you can, get a copy of The SAS Survival Guide for both bush/forest shelter and trapping/fishing.
Soap: public toilets are no longer the place for this type of thing - they use liquid soaps and hand sanitizers. Get the hard varieties (oatmeal preferred), the soft/cutesy varieties turn to mush. Use in the hair as well, you don't need shampoo. When it's warm swim in the ocean/stream/pond/lake/river (so long as they aren't polluted to hell).
Teeth: *do not forget toothpaste and toothbrush*. You can get by without flossing for a few days to a couple weeks, teeth/gums going bad will really screw you though.
Hand sanitizer: use before cooking, after loo, to clean utensils. Being. Sick. Sucks.
Sanitizer wipes: use on utensils and to wipe yourself down every couple of days. Especially the "intimate areas". Being. Sick. Sucks.
Sanitation in general in the boonies: have a folding shovel in the car. Don't forget toilet paper - sometimes available facilities run out.
Cooking: butane cook stove, basic camping cookwear, learn to use a Dakota fire hole. (Waterproof matches are preferred over a lighter - learn to use a featherstick and find yourself a decent flint striker. Have a sharp hunting knife and a means of sharpening it.)
Water: this is going to be your biggest hassle. Filling up at the local toilet is not a good idea sanitation-wise. It may not even be possible. Look for taps around the back, there may not be a handle though (specifically to stop assholes from wasting water all night - keep a small crescent in your car). If you're camping/rural, many places have free water for campers and camper-vans. If near a stream or river or pond or the like, you will either have to boil water for 10 minutes or use some form of filter or use water-purification tablets. Or just buy in 10 liter lots.
Large all-night Wal-Mart's, K-Mart's, etc: warmth, bathroom facilities, dumpster-dive for food, park the car as far away from the entrance as possible (like employees) so you can kip down in it for a few hours without being hassled.
Abandoned buildings: you need a sheltered place to sleep/stay. Watch out for rats, strays, and assorted vermin. Pick a place that isn't going to fall in on you in the middle of the night.
Emergency food stash: generally for camping/emergencies. A week of tinned food is cheap per person. Some ideas:
* Uncle Ben's rice with a tin of tuna
* some form of prepackaged heat'n'eat meal (I keep a few Kaweka Food Co meals around)
* potato flakes
* tinned stew, beans, spaghetti, fruit
* powdered/UHT milk (powdered is better IMO, though I've not used milk when camping at all)
* dried meat/beef jerky (cheap to buy in America/Australia, I make my own in NZ because they charge the earth)
* dried fruit (currents/raisins/sultanas, nuts, pineapple, papaya, etc)
* couscous (just soak in boiling water for 2-3 minutes - if still hard, add a little more boiling water)
And that's enough from me on the subject, have fun testing this stuff out.