Spread by saliva and blood? Then there's little point in fighting - blood spatter would get everywhere. If you even slice up some ground hamburger, you're likely to get some flecks of blood on you.
I say I'm going for protection first. Namely, some sort of quarantine-type coveralls, with gas mask. We're talking the thick, military issue kind of deal. Underneath, I'll probably wear some sort of thick padding, and then under all that, a drysuit for good measure. Uncomfortable, hot, but protected.
The obvious solution would be to get onto some sort of plane or boat and find some island without any zombies and try to wait it out. As I said, it's pointless to go hand-to-hand when any fleck of blood spells your doom. And guns are awesome and all, but a) you'll run out of ammo and b) if these creatures can survive without eating, then you can't assume that targeting their brain or organs or musculature will do anything to stop them from moving.
Equally pointless to go to the countryside - if they don't die of starvation, then they're not motivated by hunger, so they won't be following the food supply.
Of course, any hypothetical zombie scenario would just highlight the impossibility of a zombie. How can a blood-borne virus be transmitted so easily? How come these walking dead don't decay rapidly with exposure to sunlight, oxygen, and millions and millions of bacteria? How come they don't all get eaten by carnivorous animals (and even more scavenging animals)? And if it's because the animals turn to zombie too, then how can this virus be transmittable between all species? And if animals do turn to zombies, how come we don't see people getting pecked and nibbled to death by songbirds and squirrels in the movies? And how come the zombies don't attack each other? No, seriously - one moment they'll be biting and eating each other, the next "oh, he's a zombie, better stop." If they're motivated by hunger, there's pounds and pounds of dead, shambling flesh all around them for the eating. If they're motivated by rage, there's many people around them still moving that can be attacked repeatedly. Instead, zombies work together. Why?