Guuhhhhhhh don't get me started. In terms of mechanics you probably want to dismiss me as a rambling old man and move on, 'cuz I'll probably start delving into inconsequential minutae. But I think I can be a
little bit useful here. Like
Syril I'm working on my own system but I discussed post-apocalyptic with a friend at some length, largely on the world-building side. A lot of it comes down to what supplies are available. Verdict is, you're going to have to decide the
trajectory of humanity after the disaster, because while you can widely allow for
regional variations, as premises these settings are mutually incompatible:
- Temporary Crisis (28 Days Later, The War of the Worlds): A wide-scale temporary (?) crisis. Survival is the first priority, followed by either escape or resolution, because there is no long-term industrial impact. Anything available today IRL is available to the characters, if they get to it first. Running out of food presents an immediate problem in terms of endurance or sustaining the weak (children, sick, elderly), but whether or not starvation's a concern depends on if the characters know how long the crisis is going to last -- usually they don't. This campaign will be largely driven by fear, hysteria, and pandemonium.
- Recent Collapse (Living Dead series, Interstellar): Humanity is screwed, but this is basically in progress. Industry is disrupted and probably will never recover. Humanity is doomed to decline to either subsistence or extinction, so there's little hope (although communities will try). Again, whatever's available IRL exists in the game, BUT the transience of material goods will soon be intensely felt. Fools will follow an ever-belated progression from fresh food & bottled water to canned food and water purification to survival gear and copies of Foraging for Dummies. Modern technology will function for some time, but as fuel runs out, parts wear out, and supply chains disintegrate, supply & demand will be highly unstable. Take, for instance, an assault rifle. In the first few days of Armageddon they will be in screamingly high demand for their ability to fire common ammunition so you can take others' stuff. But as consumed ammunition isn't replaced and parts wear out, they will eventually become worthless. This won't be even, so one town's junk is another's treasure and such.
- Permanent Collapse (12 Monkeys, Canticle for Leibowitz): Humanity's been screwed for a long time. 12 Monkeys is a typically Gilliam-esque absurdist take but the main idea is that the disaster happened so far in the past that the state of humanity has re-stabilized into a dystopian hell, with any hope of recovery well beyond the characters' lifetimes. Functioning modern tech is either worthless (cell phones), literally buried treasure (people "mine" concrete for steel in Canticle), or essentially Clarke's Third Law (consider the implications of a discovered nuke, for example). As in "Fiat Homo" (Canticle), modern tech may be treated as mythological, even feared. Campaign plots would be either intensely local feuds as rival factions war over what's left, radically ambitious plans to restore humanity (12 Monkeys), or a timely discovery shaking up the status quo.
- Ambiguous Collapse (The Last Man on Earth, Waterworld): Similar to Permanent Collapse but based on either extreme denial or tangible evidence, it's not completely accepted that humanity is wiped out and/or the entire planet is FUBAR. The answer to that question is a campaign-ender and so has little consequence to the journey. The practical difference is that while the above collapses have some semblance of society (even if in chaos), Ambiguous Collapse is about extreme isolation and holding out hope that there are others to find. In that sense it's actually more similar to Temporary Crisis, except whatever event fragmented humanity happened generations ago. As such, the party is sustained entirely by foraging whatever remains after repeated lootings and the passage of time. Things can get quite gritty; the back-up weapon to a bolt-action rifle might well be a handmade spear or shiv.
- Partial Recovery (Mad Max: Fury Road, Nausicaa of the Wind Valley): Same basic premise as Permanent Collapse but instead of a humanity-has-no-future take, people have partially re-industrialized so some forms of modern technology remain available (namely cars & guns in the case of Mad Max). However, the unevenness in which communities recovered has resulted in mass migrations, famine, war, endemic inequality, and brutal fiefdoms. Despite actually having a future (in theory), the Partial Recovery scenario is more tangibly ugly than Permanent Collapse because the availability of industry feeds political instability & petty ambition. Warlords will scorch precious resources out of pure greed ("mine") or malice ("not yours").
I bring this up because I sense you'll need to reconcile whatever system you're considering with the campaign tech level. These days the trend is to just make everything a pie-in-the-sky abstraction so I anticipate little mechanical impact; the question is whether folks are killing each other with assault rifles over canned food or with handmade spears over a handful of seeds.