See, now this is exactly why I come to this forum. For hard-hitting, serious minded, deeply philosophical questions that matter. Also, to be around other people who relate everything to style and accessories!
So, I have to say, I really like your thinking. A backpack, crossbody, and tote do indeed seem to be very sensible. Although, I might skip the tote unless my husband carries it, because those get heavy. Also, I'll need my hands free for wielding weapons to whack zombies. ALTHOUGH now that I think about it, I do have a patchwork fabric tote that has a very long handle and could be worn crossbody in the back (under the backpack) if needs-must.
I don't actually have a good backpack. I have a few handbags that are worn on the back though, so I guess one of those. I could use one of the kid's backpacks since those are roomier, but those are so ugly and even in a zombie apocalypse I need to have standards. Oh no, wait! My daughter's backpack from last year is a cute Betsey Johnson. Pale pink with deeper pink hearts embroidered into it. It's a little childish but either she or I could carry that one.
For my crossbody, I'd have to go with the Dooney and Bourke yellow Wayfarer that I just got. Technically it's an over-the-shoulder, but it's so roomy and I could lower the strap. Although maybe wearing bright yellow would make me too visible. Hmm. Well, I don't have it yet so I don't know how it would fare, but I ordered an Owl from Frrry which might work. It looks roomy and a good combo of easy to access without stuff spilling everywhere.
Wow, this thought exercise has made me realize just how many bags I got rid of in my recent bag-purge. I sent a bunch of unused stuff to charity and now I barely have anything useful left. This is terrible. I mean, what if there's a zombie apocalypse and here I am with no suitable bags! I think I'd better go shopping asap!!
We are also watching The Last of us, and we watched The Walking Dead from season 1 to final season. So believe it or not, I too have pondered this very same question.
Although I agree with backpack and crossbody, I am going to have to pass on a tote. Running could prove problematic with a tote. Personally I am going with my Hermes Herbag A Dos backpack. That will proved virtually impossible for anyone behind me to reach in and steal my beef jerkey and other essentials. Crossbody will be my Hermes Evelyne 40, otherwise known as "BABS" or Bigg A Bag. It will hold a lot. Of course as as @880 said, I will keep the H logo inside so as not to drawn unwanted attention!![]()
This is why tPF is the absolute best place. Not only am I assured that I am not the only one to have considered this, I am getting great tips on some great factors I had not considered.

If I were to repost the original post, I might have added a poll: Take cute bags because the world is ending? Or take functional bags to stockpile supplies?