Relatively new scripter, need help on a Chase Script, any advice?

This is the thought process I would recommend following when you complete your scripting tasks:

What are you trying to achieve, and what tools are available to you to do this?

Well for starters, you have a MoveTo command, a magnitude calculator, and a list of players along with their characters and torso positions.

What could cause errors?

If someone's character, torso, or humanoid isn't present, this may cause an error, depending on what is needed.

Iterating through players seems like it will be necessary, so a "for" loop will most likely be used. You'll want to put this into another function so that it can be called for the MoveTo command.

I would recommend setting up two variables, one for which object is closest, and another value representing how close the closest object is. Each time the for loop looks through the characters, it should compare distances to determine if someone is closer than another.

When all of this information is put together, you'll come up with something like this.

local hum = game.Workspace:WaitForChild("Zombie"):WaitForChild("Humanoid") -- I'm assuming hum is some NPC-type creation, so I just wrote this for granted.

function nearPersonPos(obj)
	local closest = nil
	local bestDist = nil -- If you want people only within a certain stud range to be detected, you can make this an actual number for that stud range.
	for _,v in pairs(game.Players:GetChildren()) do
		if v.Character then
			local tors = v.Character:FindFirstChild("Torso")
			if tors then
				local dist = (tors.Position-obj.Position).magnitude
				if not bestDist or dist<bestDist then
					closest = v
					bestDist = dist
				end
			end
		end
	end
	return closest
end

while hum and hum.Parent and hum.Parent:FindFirstChild("Torso") do
	hum:MoveTo(nearPersonPos(obj) or hum.Parent.Torso.Position) -- If the function doesn't return a person, make the NPC's destination his own position so he doesn't move.
	wait(1)
end

Keep in mind this will NOT pathfind for you. To do that, I would suggest looking into the other answer's wiki article link, or even look into some A* path-finding algorithms of your own; they can be very fun to use.