Different types or just variations?

Well the types of zombies you're going to create depends on what is the reason for their appeareance. Seeing it's a disease-based contagion system, traditional zombies are the easier and cheaper way to do it in their appearance. It's easy to have bloodshot eyes, bits of flesh missing and death palor.
Regarding movements, slow zombies I think make it boring unless they're in large groups, which adds strain to a budget. And make-up and SPFX will cost you an arm and a leg if you want good quality + long shots. Get them moving fast, like feral creatures. That would put stress on the people fighting them and give you some ideas to play with, like zombies as rats in the giant maze of a city, still intelligent enough to try and break out. Thus threatening to infect the rest of the population. Would probably work well with a District 9 type of shooting.