The advent of computers enables us to store a whole lot of data very easily. As such, I would minimise the books (I love books, this would be a necessary tragedy) to great works of fiction and technical manuals on how to build generators. For the computer I'd have installed, there would be no password login and a picture-guide to getting information. There would also be every tome available in a variety of different languages.
To power this whole shebang, solar panels and a build-your-own wind turbine complete with picture-book instructions.
For transport I'd have two bicycles and plenty of repair supplies for them. One off-road bike, one road bike. As fun as motors are, generating fuel post-apocalypse would be difficult. I could also include an electric scooter due to having a solar generator. Push-bikes are quieter, always an advantage when trying to avoid attention.
Non-perishable foods are fantastic. Mountains of tins would occupy all the available space around the aforementioned stuff. There would also be a couple of can-openers. A custom-built water tank would fit like a doughnut around the inside of the entire container, about 6 inches thick. This would be plumbed down to a tap near the door. There would also be water purification devices like a store of flocculation chemicals, filter equipment (charcoal and sand work well for this, actually), etc. and a roof-mountable series of condensation collectors. These would probably be plates with a well in the centre which extract moisture from the air that then trickles down to a collection tube. Dry-sealed seed stock would be carefully catalogued in a book and added, in sections, to the container. Possibly slung from the roof or tucked away, hidden. Some pots and pans too. A grating to sling over an open fire to make them easier to use.
Camping gear is fantastic. Few sleeping bags, a tent or two, self-inflating sleeping rolls for hiking. Compass and several topographical maps of the area which could help depending on how bad the apocalypse gets. Are we talking nuclear apocalypse or Exterminatus? How about 'nids? Zombies? 'course, you can't tailor-make this.
Self-defence would undoubtedly become an issue. Catching more food too. A hunting bow and a good stock of arrows, along with fletching equipment and detailed instructions. A Japanese master swordsmith-made Katana. Hunting knives, skinning knives and a good pocket knife. I'd also put in all the necessary care and sharpening equipment. Guns are limited by their available ammunition, but I'd still include a hunting rifle and a hand-gun with sizable ammunition stock for each.
I suppose "miscellaneous" covers the next bit. Lots of rope, both natural-fibre and synthetic, of varying weight. Picks and shovels. Some steel buckets. A variety of sizes of bad weather wear and boots. Paper and pens. Large first aid kits including basic surgery equipment for setting bones and removing shrapnel. And of course, instructions. A harmonica. A few steel camp chairs.
That's all I can think of now, I may add more later.