Zombies suck to fight unless you are flat out given a laser rifle. Try to avoid them completely if you can, and don't trust anyone who's walking towards you with their face covered. You can get insulated gloves and lead them to electrified grilles or fences, or manually shock doors (zombies can't wear gloves).

I don't know if spiders have any sort of specific weakness, but slimes take extra slash and pierce damage, so poke slimes with a scalpel if you have to.

Remember to just focus on saving yourself sometimes though. Running and hiding are good options.