I'm trying to make an action scene, where zombies run down a hallway. But I need a way to make a zombie run in a straight line in vanilla minecraft. (And possibly wearing armour and a player head!}
As far as equipping the zombie with armor, you can spawn it with the
/summon command (a nice explanation of how to use it can be found here).
With regard to getting your zombie to move in a desired direction, I would try spawning a villager in the direction you want the zombie to go. They tend to chase them.
New updates also include invisible blocks called barriers, so you can limit their paths with those.