ZOMBI

Since the difficulties don't stack there's no reason not to do this mode first. It isn't that hard but don't try to play it as if it were Left 4 Dead because any zombie can take your health down very quickly if you aren't paying attention. My main advice would be to take it slow, be systematic and never be afraid to retreat or backtrack to the Safe House to save mid mission. Some other tips with minor spoilers

When you see several zombies ahead of you, try to sneak forward until one sees you, deal with it then tempt the next one in

Zombies can often be killed in one hit when manoeuvring past something. So wherever possible go back through a door, over an obstacle, up a ladder etc and just take them out as they try to follow

In the room where the zombies disco, do not turn the music off and they will remain oblivious to you

Watch out for the exploding zombies who carry gas tanks and make a hissing noise. Whatever you do, do not melee them.

When you encounter electric zombies, back yourself into a corner and let them come to you

The Arena was for me the hardest part of the game. Run around until the zombies are grouped together then shoot one of the propane tanks/the exploding zombie. Save a mine for the end and place it by the metal gate before you press the switch

Planks are a complete waste of time so don't waste precious space with them

Flare on the other hand are very useful. They will distract an entire group giving you time to escape, or throw a grenade/Molotov into their midst

Don't lay mines when zombies are chasing you because chances are you'll get caught in the explosion

Ammo will still be scarce on this difficulty so save it for when it's really needed. Not sure if it's a glitch but I could never zoom with scoped weapons, making them pretty useless.