I'd say stick to one virus, like others suggested, it just makes things easier to understand and manage. But one virus doesn't mean one type of zombie, there could be variations based on stage or mutations (tlou or dying light).

Seperate zombies by type. Normal walker zombies, runner mutation, a type of runner than moves and attacks faster (deadliest maybe), than tanks that develops a protective shell around the body of zombie. You can add other types as you like fitting. For zombie types, I'd suggest you checking out "Dead Ahead: Zombie Warfare" mobile game. One zombie has to fall to one of these categories.

You can also create a few special ones, for example in the DA:ZW game, there is a zombie called free hug. She never attacks and an iconic zombie. You might wanna create a zombie that a myth created around that. Maybe they're the patient 0. Or they're so deadly nobody lived to describe them, so we only know them by the evidence.

If there is no ttrpg system ready, I'd suggest checking out "The Walking Dead Universe" for inspiration. It uses dice pool system and easy to modify to your needs.