A real scare factor for me IMO would be when something forgets up at precisely the wrong moment; Having your gun suddenly jam when you round that corner and face the big scary thing to shoot can be a good 'oh stuff forget' moment in some cases.
Ammo and guns are going to be extremely hard to come by. Most of the time, the two most reliable things you'll have on you are melee weapons and a small firearm. The few zombies staggering around will be extremely powerful, fast and hard to take down, so facing them head-on is not a good idea.
I want the players to start off feeling weak, that way it empowers them when they accomplish even the simplest of tasks.
When it comes to the 'eerie' feeling, ambiance can do quite a lot. Having some form of 'sanity' come into action can also really unnerve some people because they're not really sure if that thing over there's real or not.
That might be something worth looking into, having low sanity causes you to hold less weapons or in worst cases, cause "blackouts", making you pass out and be returned to the nearest safehouse or something.
When it comes to ambiance, the best thing to create an immersive ambiance is sound design. Sound design will be a heavy thing, and I will make sure it's easy to install all the sound packs for the full effect!
With zombies, you really want to have a varied box of them. You can't just have everything and everyone be your run of the mill 'i'm going to stagger towards you slowly!!!!!!!!' undead; it really pays off to have things where they seem not only cosmetically different, but physically different as well. I don't mean things like 'oh this one shoots spit at you' or whatever(although that is acceptable enough), I mean physically different as in 'oh forget stuff that's an undead version of the loving hulk, and all I've got is a loving wrench' kind of different.
I was thinking about having "stages" of zombies, where zombies start of extremely strong when they've just turned, and get weaker as time moves on. Strength comes in waves, so when a new zombie horde moves into an area, they'll be tougher and in larger packs, whereas in the areas with older hordes would have weak zombies and fewer numbers.
Also I'm thinking of putting RDMers (Random Deathmatchers) into the role of the special infected. That way they can have their DM without ruining other people's fun.