Matt Colville has this video with some good advice on the logistics of running monster encounters. It also introduces a new PC role: the "monster wrangler" who is responsible for assisting the referee in moving the monsters and tracking their various abilities etc.
Colville also has this video where he recommends having PCs track the damage they've dealt to monsters, which I agree with (I also have PCs record and track initiative). If you're concerned about resistances and the like and aren't able to wrangle the mathematical tool Colville describes, you can have the PCs use 3 colours to write down damage. Blue, black and pencil works fine. One colour should be damage types they're weak against, one types they're resistant to, and one colour should be damage that's neither. You can change up which colour is which from each encounter so the PCs don't automatically know that "blue" means "bonus damage".
This is a good addition to the list of possible PC roles you can use, which currently runs: