I always use a bicycle with fenders in the rain. There's usually not much reason not to, the weight penalty isn't all that big and the supposed aero penalty pretty much doesn't exist. They keep everything far cleaner.

Might depend on the condition of your roads, though. Riding on wet roads without fenders here often means getting covered in grime.

The one drawback is that it's hard to pull off a good "fenders" look with modern bikes. I've dodged that issue by having multiple fendered vintage bikes.

As far as waterproof shoe covers go, the important thing is that you have waterproof leggings that come down over the shoe cover. Otherwise the shoe cover will be somewhat ineffective.