Without having to custom-build anything, the easiest way is to add the catalog category widget to the homepage.
From the homepage, Add content > Catalog Categories (in left column) > (select category in middle column) > Category Items
If you want it to be the only thing that shows up, create a new Catalog Category, add it to your catalog item, and then pick that category for the homepage.
If you're dead set on a button, you would need to make a static Content Block within CMS that had an HTML button, or something along those lines (harder to maintain).
