The zombie genre is the most over done, but still one of my favorites! I think a big part of making it interesting and not like everything else is your characters. The reason I tend to love zombie stories and shows so much is because of the characters fighting against them, trying to survive. Coming up with creative ways for the outbreak to spread, how the zombies behave, and how survivors fight them is how you can create your own world of zombies that stands out too.
Two of my favorite zombie shows are Z Nation and the Walking Dead series (spin-offs too) Though, sometimes I'm not a big fan of all the Walking Dead seasons. I won't go into detail about the show's flaws here. While the Walking Dead takes on a more tragic and serious vibe, Z Nation relies on comedy and crazy characters. There's even a scene where a stoner gets trapped in an elevator shaft with a zombie and gets it high.
My good friend on Wattpad Crimson_Graves has a really fascinating zombie story too, where the outbreak starts with animals, which begin to infect people as well. Zombie deer and dogs are definitely not too common, but really cool to see how it also infected animals.