Lots of people sneer at the dollar stores, but they have a lot of stuff to get a beginner started for a reasonable price. Cheap is worth a lot compared to having nothing at all.
Start with a cardboard box. Put a folded newspaper in the bottom.
Put TeacherRO's (above) first aid kit in it.
Then walk the aisles and see what they've got for a short-term emergency:
Bottled water (gallons)
Alcohol antiseptic gel to start fires
Foods that don't need to be cooked: granola/protein/fruit bars, peanut butter/crackers, canned juice, tuna, chicken, fruit.
Can opener.
Paper plates, cups, plastic utensils.
Add more first-aid when you can: gauze pads, antibiotic salve, cleansing towelettes, adhesive tape, hydrogen peroxide, tweezers, latex gloves, rubbing alcohol, more bandaids. Get small containers of meds you usually use: anti-diarrhea, antihistamine, pain reliever, antacids.
Flashlight & batteries (splurge on decent batteries if you can).
Cleansing items: washcloth, towel, bar soap, toothbrush/paste, small shampoo, TP.
Tools: pry bar, a couple of screwdrivers, pliers.
Safety: dust masks, plastic goggles, extra reading glasses.
Pet stuff: Leash (check for weak clasp), sturdy collar, bowls, plastic bags for food.
People who have a nice little kit built from dollar store purchases are still far ahead of most Americans who think that nothing will ever happen to them.
Sue