I am beginner at learning after effects and after learning the basics about animation and shapes layer I found that very quickly layers to many very quickly. One think that helped me in managing them better is to hide layers which I am not working with and showing only the ones which are important.
Two Techniques that worked best are.
1. Show/hide properties
2. Shy Layers.
Suppose you are synchronizing the animations and you only want to see the layers which have keyframes, you can select the layer and hit U key and it will show only the layers which have key frames. I loved this because it clears out all the unwanted layers at the moment.
The following is an excellent tutorial on youtube by Josh Short that explains more shortcuts that can come handy.
Sometimes you might want to work only with two layers and hide all the others and this is super easy and very helpful to remove the complexity while editing a few layers.
See the following tutorial by Baker Tuts.