Too many variables here to give one answer. My first thought: Do we maintain a safe source of freshwater? That does not have to be from the faucet. I can drink from a lake. So do I need to hoard it? Or will nature take care of it for me? Secondly, what is our food production like? Rice and Beans can keep you alive for a long time, and store well. Food and water - those are my first two thoughts. That may be in the form of farming, fishing, hunting, and trapping, but I'd need to take care of that. Then I'm thinking medication and medical supplies. Penicillin, painkillers, aspirin, bandages, sutures, gauze, tape. Maybe some cheese, it can pull double duty as an antibiotic and a food. Condoms. Wouldn't wanna have to deal with a little one running around.
Ok, that stuff - the bare essentials - is taken care of. Next, I'm looking at fancy footwear. Wool socks, numerous pairs of quality insoles, enough boots/shoes/sandals to last me 2x however long we think this is going to take. I'm stocking up on blue jeans, sweat pants, longjohns, jackets and shirts, some nice hats and gloves. A lot of wool and leather, and a lot of high quality stuff that I normally don't bother with.
Next, firewood, and other things with which to make heat.
Then, tools. Whatever I think I'll need to build, maintain, repair everything I have. Same with hardware.
Somewhere in this list is enough fuel to get me 2x as far as I think I need to go. Probably 1,500 miles worth. Not sure if it'd be necessary or not. I'd want to go north to some areas where I'm reasonably confident that we will have an abundant natural source of clean freshwater.
But again, we don't know what kind of apocolypse this is. So all of this could be stupid.