In a true apocalypse, zombie or otherwise, one of the main difficulties you'll face is the lack of power. What good are high tech tools when the lights go out?
Yes, you might be able to generate a little power with portable solar panels. You might be able to lug a generator around, but you've got to keep it fueled. My bet is that just a few weeks after a true apocalyptic event it may be increasingly difficult to use anything electrical.
The best thing to do when the lights go out and you're fleeing for your life is to go low tech.
Really low. And for an excellent selection of low tech make a stop at your nearest antique shop.
Most antique stores have boxes of old hand tools intended to be used in decorating. Use them as tools. You'll also find lanterns, but better than lanterns would be candle molds. Want to keep shaving? Look for antique straight razors (and then learn how to sharpen them or you're better off bearded). You might even want to haul away a manual typewriter if you want to keep a record of your survival, but I'd recommend sticking with pen and paper for much better portability.
Antique stores are a gold mine for the survivor. The things in these stores have already demonstrated their own survival capabilities. They might just help with your own long term viability.