Speed is the path to supremacy, so Agility would be the most important without a doubt. Rather than upgrading stats which would make you more resilient to injury and infections, it would be much better to not get injured in the first place. A build based on speed would not only make dodging zombies easier, it would help a lot in running from them and even killing them faster; moreover, more speed equals more power because of the kinetic force behind it.
Stamina. You won't get many resources, like food and water, always on your feet, you gonna need stamina honey, unlesss your a cheat. Or in some bunker or safe zone
I think it rather depends on the situation (like what kind of zombie apocalypse and what you are working with in general), though viral immunity or at least resistance is always useful (though being physically tough doesn’t guarantee immunity depending) especially depending on the way of transmission (you’re screwed if it is airborne and you aren’t resistant). I’m just going to rank the stats as physical, mental and social I suppose. Physical can help you fight and survive and is especially useful if there is little in the way of advanced weapons and you’re mostly working with rocks and such (can get especially crazy if it reaches super human levels). Mental can help with making and fixing weapons (or magic if it is that kinda world) and planning. Social can let you rally others around you to survive (why fight with one when you can fight with many), which will be indispensable unless you are a superhuman badass that doesn’t need others. None of this really answers the issue, but I can really only say that it depends on the scenario and what you’re working with in that world.
I'll break down the stats you listed and how much they are worth: Strength - Decent to get through walls or barriers and you might want some but it has little benefit due to it having high consumption, you would need a lot of constitution and stamina to have actual super strength to the point you can crush anything of value. Agility - Again like strength, some agility to handle a single zombie with ease would be nice but beyond that usefulness goes down if you get swarmed. Constitution - Having a high constitution is nice, but the benefits again fade as it goes up, you really only need enough that they can't bite through you easily, but beyond that if you get swarmed you are pretty much stuck even if they can't hurt you Stamina - This might be the most important stat, you might go days without food or water and might need to run for miles to escape. If there is a stat that you might want to go highest on, that is stamina. The biggest risk for a zombies has always been when you go out for supplies or leave your safe area. If you can go a year without food and water, that would definitely play to your advantage. Intelligence - This stat is also important, but the benefit beyond a certain point decreases as zombies aren't being of logic, of course if you get intelligence high enough you might even create a cure, but you have to live long enough to get there. So what do I suggest? A balanced build with preference into stamina, once you get to a point where you are safe enough, then you can go into other stats be it intelligence if you want solve this issue, or combat stats like agility if you want to feel like the hero and slaughter them.
Stealth all the way. If they don't sense you then you don't need any other stat other than end because you wont know when you next meal will be
Constitution and vitality may be the same, though I imagine constitution being more of a tank stat that makes you burly, while vitality is regeneration so that's mostly for vampires or some that can regenerate limbs without having to be big tanks. Then you can be big and tanky or regenerative while still getting out of breath, that's stamina. So my answer is stamina being most important because you have to always be on the move for supplies, on the run from zombies, in the fight with them as they try to swarm you. You need it whether you're ranged or melee.
So in a world with regressing technology, scarce resources, failing machines you'd increase your intelligence to try and invent new technology which requires dozens of people to develop and produce over years with plenty of money or resources and information, internet is ofc down, electricity too. You think high int is required for foraging and weapons maitenance? What a waste... you'd die first coz you didn't invest in stamina before you even learned something actually useful and highly demanding of intelligence.
According to this, cardio is the most important. So in the order of importance, the stats most important, are stats that govern these traits, in order: 1. Stamina 2. Carefulness 3. Insight 4. Wisdom 5. Charisma 6. Preparation 7. Agility 8. Chastity So adding together, the most important stats, in order, are: 1. Wisdom 2. Constitution 3. Charisma 4. Agility 5. Chastity 6. Strength (to bash zombie heads with a baseball bat)
With high enough intelligence, who knows perhaps, I will invent something new, something earth breaking, something that will change technologie as we know it, I will be like those crazy genius scientists in anime or manga who will make something that leaves other people wondering how, I will be a genius above all geniuses, (I just don't want to stay 'in a world with regressing technology, scarce resources, failing machines, internet is ofc down, elictricity too'), perhaps, I will find a way to make something like those force fields that will make a person freely travel in space (like the silver clan in heroic age) or perhaps, I will make a gundam with high specs and maybe a never ending energy core, or perhaps, something like those creatures and mechs in Suisei no Gargantia, etc... With high enough intelligence, I might even become a powerful psychic and get several OP abilities like travel between time and space, the possibilities are endless... I just refuse to stay on a pest filled planet, with people panicking and moral degrading, scarce food and drinkable water, whatever reserve people will prepare, will end sooner or later, it will be apocalypse and the human race will disappear. That's why I prefer terraforming or finding someother planet or world to live on (who knows maybe it will be an isekai )
All I'm saying if everyhting stays realistic except for zombies and system, anime science would be impossible.
Mate you already made an exception for zombies and system, make one too for the anime science as they all fall together under the same category of being unrealistic and merely suppositions