Category display options

We’re trying to create a menu based on catergories. We’d like to control how the results appear when a user clicks on a category name in the menu. Right now when a user clicks on a category, each entire post from that category appears. That’s too long for our purposes.

For example if this is our menu:
Texts Music Language Nation

when a user clicks on “Music” we’d like the results to be all the excerpts of posts categorized as music, not all the complete posts with the category of music.

Are there ways to make the excerpts or a post title appear, preferably with an image?

Thanks in advance!