How showing the pages inside a specific category (without coding a new template)?

I've a Wordpress site where I'm using "posts" for news and "pages" for some static information pages (about, contact, ...). Now I need to add a bunch of pages: one for each product that I sell. Also I need to add them in different categories (i.e. T-shirt, Pants, Shoes, ...).

The problem: In the frontend I need to navigate to a page that lists all the products inside a specific category. And I don't want to create a page myself using code/html/php because I bought a theme and I want to use its templates (otherwise I need to re-create all the layout, styles, etc...).

I tried to add categories to "pages", insert products in a category and navigate to http://localhost/mysite/category/t-shirts/ but it doesn't show any pages. I could consider to use custom post type but, remember, I'm here for have the most simple and fast solution to my problem!