A lot of folks are saying what they would hoard if things go bad. That's funny to me. If I don't have it already, I'm not going to get any of it when all of a sudden everyone else wants the same thing.
For a week or two (tornadoes, bad winter storms, maybe the New Madrid Fault decides it's time to let loose again), the goals are just riding it out until conditions stabilize. In that case, Fuel and canned goods are handy to have on hand.
If it's a more permanent thing...that's a different story and I don't think hoarding supplies will be as important as knowing what you're good at and being ready to put that to use cooperatively.
I live on a few acres which is nice but the real concerns if things got very bad would be water and food. I wish I had a well, but I don't and I'm probably not going to spend $10K (or whatever it costs) to have a well drilled just in case. There's a creek full of farm runoff that touches our property at one spot. We could boil water to survive. I'd start collecting rainwater right away, too. I'd like to have a sustainable way to make potable water from a mud puddle. I think a plan for purifying water is important. I would like to act on this.
I learned of a Birkey filtration system in the past. I need to re-familiarize myself with it. I don't think it's completely apocalypse-proof...but it would be a good thing to have for a short- to mid-term fiasco.
I haven't put together a plan for food, but I do feel it would be smart to have a couple weeks worth of "it'll keep me alive" stuff like beans, rice, etc.
If I had to feed myself long term...it would be pretty bleak, at least to start. My wife would probably grow some vegetables if the catastrophe happened at a convenient time of year. But we don't have canning jars, or any actual experience canning or "putting up" food. I could shoot squirrels and deer and stuff (I don't have a deer rifle, actually...maybe that's something to think about) but I'm not a hunter. If I was hungry, I'm sure I could survive, though. It's more likely we'd try to network with foodies who need some skill we have. In an apocalypse, they'd call me MacGuyver, no doubt.
We have plenty of leaves for toilet paper, I guess.
My wife has a horse and a mule. Those would be such a huge liability in a SHTF situation because they're modern horses that need chiropractic and supplements and all that. I'd turn them loose when she wasn't looking if I thought they'd run away...but they wouldn't. Seriously...they'd just eat grass and drink creek water and be of zero use other than maybe riding around to network with the neighbors. NOBODY should go out and get a horse for a cataclysm. As a non horse person living with horses, I am in a very good position to tell you this is near the top of the list of bad ideas.
I can spend all the time I want preparing for the wrong type of apocalypse. Might as well plan for realistic ones like when the electric and water shut down for a week.