Cards that give +1/+1 counters are great when only your creatures are targets, but if you are trying to help get rid of a particularly annoying creature, you may not want to be giving your opponents creatures permanent bonuses
Instead, a more reactive control build is more suitable especially as it has a lot of space to diversify its trap lineup to cover many matchups
As a land that enters tapped, Zanarkand, Ancient Metropolis will always be somewhat slow
Not only was the card banned in Modern for a while, it was a part of one of the most not real Magic decks in the games history: Legacy Manaless Dredge
But just once per turn, but note that that could happen on opposing turns, so artifact dorks with flash or flash enablers that are colorless are great for this deck or in the 99 of other decks
Drop your decklist into the deck analyzer to check your curve and zombie-payoff density before you sleeve up, and browse community zombie decks for proven lists to copy