I am all about embracing the idea that you're going to get wet when running in the rain, but that doesn't mean I have to be uncomfortable. I wear a light running jacket that kinda repels a water but is more of a wind shell. It's great for giving me an extra layer over my regular long sleeve shirt and is better than wearing an all cotton hoodie that is just going to soak up the rain. Light weight also means that it won't get heavy when it's wet, which is what you don't want.

When it comes to legs and feet I don't bother protecting them, they get by just fine.

Look for something packable so it isn't a big heavy coat, like this one from amazon. Not water proof by any means, but slightly water repellant for a bit makes a big difference on my runs.