It actually PREFERRED to use butchers in evil lands- butchering a corpse/limb prevents it from resurrecting. I have heard of zombie hairs though, but haven't run into one myself. For hte most part, just don't use axelords. They tend to triple your zombie chances. Also, don't use macedorfs: Warhammers are superior to maces in every way. In fact, a silver warhammer is superior to an adamantium axe... except against bronze colossi and other large beasts. Silver is triple the density of steel and warhammers have a very narrow impact zone. Combine the two and all that weight gets concentrated in one spot for maximum carnage. Silver warhammers will often kill a humanoid target in one hit by crushing their skull in. Silver will mostly bounce off a bronze colossus/ bronze+ forgotten beasts though. Larger creatures (hydra's/dragons) benefit more from spears (since a warhammer won't reach the organs of such a large creature).
About your depot- that is a good idea, but it won't force your caravans to arrive next to its opening. Your caravan could spawn on the opposite side of hte map and die from acid rain (then reanimate) before it reaches your tunnel. Reanimation isn't immediate, but it is a feature of ALL evil biomes. In a way, this is fun for training your military. Military smashes zombie... zombie reanimates! Military smashes zombie (again). etc.
Also, that acid rain will actually coat your dorfs. You need to set up a (cleanable) bath at the entrance to your fort. A simple pool of shallow water that they are forced to walk through will suffice. You'll want to set up a pair of pumps (powered by a windmill aboveground) to clean the water asap. It'll also create mist to make your dorfs happy. Just don't set that as a water source! The next thing you do is secure a reservoir to set up a well. Just make sure it is 2 levels deep, as a 1 level deep reservoir will be "muddy" water instead of "clean" water.
You are already rather fortunate, btw. That rain could have including a thrall-inducing syndrome (thrall's resurrect with all equipment), or you could have been immediately set upon by a pack of zombie animals. I don't you embarked with a military either... My very first evil embark died within the first month.. hell first few days, when a flock of zombie ravens decided to go all Hitchcock on my dorfs.
Absolute first hting to do with an evil biome is start with a pair of military-trained dorfs and immediately burrow underground. Once all your supplies are carried below ground- seal off the entrance. Then you forge your weapons, get your farm set up, and build that reservoir/cleaning room. Avoid using your military squad as hunters too. Kills tend to reanimate before making it to the butchers. However, a butchers right next to fort entrance(s) can help with this.
Oh, never embark on the shore of a terrifying ocean though! Zombie sperm whales are no joke (absolute largest creature in the game).