- A Bible - as a Christian this is the single most important text you can own. Use for reading, copywork and basic moral instruction. Even if you're not a Christian it should be considered a piece of classic literature
- Dictionaries - at least two and preferably more - 1 Children's picture dictionary, 1 standard Websters dictionary. A collegiate dictionary and student dictionary would be useful as well. Use for vocabulary, spelling, copywork.
- The "What your __ Grader Should Know series" by E D Hirsch. - This is a great overview of all the major subject areas. There are enough suggestions in each of these books to build your own curriculum on. I have been able to use the Kindegarten edition to talk with my 5 year old about many topics.
- A compendium of the founding documents. - These can be printed out from a variety of sources. A bound copy would be nicer but you can get the same information for free on the web. Every American should memorize as much of these documents as possible.
- If you can find them free or cheap, and have the space to store them, I would add vintage Readers Digests and National Geographic magazines/maps.
As long as society doesn't completely crumble you should have ready access to local libraries to supplement you children's reading. If you are concerned with TEOTWAWKI then I would add some classic novels and field guides for birds, trees, plants, etc. (please note that these are ONLY books recommended for homeschooling, my full booklist includes many other titles and subjects)
(as much of each as you can comfortably store in a small area)
A frequent good source of notepads (and sometimes desk calendars) is local printers. Call around and see if they have any. When I used to work in an office and had to run to the printers I'd look to see what they had. Usually there's a table by the receptionist desk with a pile of freebies on it. I've never had anyone question me about it. Also check your local newspaper for end cuts of newsprint. These are the end of the roll that's left after a printing. The paper is excellent for childrens art, banners, wrapping stuff in, etc. Our paper sells them by the pound. I think the last time I bought one it was under $5 and was enough to last a year or more.
THINGS TO KEEP AN EYE OUT FOR - more crayons, markers, colored pencils - ask on Freecycle or check at yard sales. Rubber bands can be had by the handful at the post office here in town. I suspect there are also great sources of free paper clips as well. Even if you have to purchase a small container of each. A dollars worth of each will last you for years.
compass, protractor, stapler, staples, hole punch - handy to have around but used infrequently. Can purchase all of these for under $10 total. I keep them in a small shoebox size tote tucked away on a shelf so I can always find them. If your children reach an age where they're using them on a regular basis purchase an extra set for them. I also keep a few solar calcuators around (all found for free or purchased on clearance).
Penmanship paper is invaluable if you have little ones just learning to write. I pick up partial pads at yard sales every summer for a quarter each. My daughter goes through tons of it.
Index cards - keep a few hundred around. These are great for making your own flash cards and are an invaluable tool for Jr High age kids working on their first research papers and book reports.
Extra bonuses - Paints, paintbrushes, modeling clay - paint brushes can be found at most dollar stores, paints go on sale in the fall with school supplies - they're a bit harder to find but they are out there. I found my pster paints at Rite-Aid on a buy one get two free sale. Walmart carries cheap modeling clay in they crayon aisle - it's been 97 cents a box for the last 3 years. I buy at least 4 boxes.
The most important way to prepared to homeschool on your own is to learn as much as you can. You can only teach your children what you know. Educate yourself on a wide variety of subjects. If you want your kids to learn American History then you need to know it. It's not impossible to teach without the knowledge but it's not enjoyable for any of you. I'm no good at science but even I can manage a field guide to birds, trees, etc. I've been amazed to realize how much I actually do know about basic science. I can identify local wildlife and fauna. I can grow plants and do simple science experiements. Books are handy but use what you already know and learn along with your kids.