Jack came back later to his apartment after relocating to the school but they lost almost everything in the fire.
Didn't he have a seperate garage/storage room...i think he mentioned something like that at the begining. But then, it's a while and i may confusing something.
Lol rather surprised in all his survivalist planning he never got around to getting a water purifier or a camping stove with a few cans of portable propane.
That and the charger when an SUV would've made better sense, roomier, can carry more, more robust for off road travel
He did stock up on all the survival/camping gear, way at the beginning of the story. He probably left most of it behind though when they had the unplanned hasty exits from the apartment and then again the school.
U sure ? He stocked food, a couple of solar lamps, some fuel and a few guns, but that was all iirc.
Camping gear, water purifier, camping stove etc. i realy don't think he thought about that, iirc it was even mentioned he didn't have some basic tools to barricade his door at the apartment and he would have problems transporting all that stuff (including larger amounts of food/water) with the Charger.
I don't think Jack had a plan at all, besides sitting it out in his apartment.
Until the infected/bandits where getting closer and where knocking at his door, he didn't plan on leaving his appartment. Not to mention leaving the city, that idea came only at the school, so i doubt he actually had stocked survival gear.
And while he spoke about his plan to leave the city, he did literally nothing to prepare for it, or scavange for survival gear and they where at the school for several weeks.
He even mentioned that he was bored, cause there is nothing to do.
The idea of getting a more suitable car didn't come from him, it was Carol and Jack was really reluctant to the point that it sounded like excuses.
At this point, i think Carol had thought more about the plan to leave the city than Jack has.
Overall i got the impression, that while he spoke about leaving the city, he never thought about an actual plan, or about essential equipment they would need.
And i'm sure, if the fire hadn't forced them out of the school, Jack would have waited there for months.
A relative safe place, content with his coffee and booze, until bandits/infected, or a lack of supplies, would have forced him to act again.