There are two ways to go about organizing your catalog.
1) You could use the Search API method that Kickstart 2 uses
For your site, you would need to create taxonomy terms that correspond to the "type" of product landing page you want. In Kickstart 2, these terms are found in the "collection" vocabulary: /admin/structure/taxonomy/collection
Next, you would want to create "sub types" of products. These are also a taxonomy and can be found here, under the "category" vocabulary: /admin/structure/taxonomy/category
Finally, you would want to create a "brand" for your products. These are also a taxonomy and can be found here, under the "category" vocabulary: /admin/structure/taxonomy/brand
Once you have your three taxonomies figured out, the trick is to create products that select each taxonomy. So a "Sony Laptop" would have the following terms connected to it: Computer, Laptop, Sony.
To make your catalog work the same as Kickstart 2 Demo store, then you will want to create a view that can handle the three levels of taxonomy terms as we described them above. For example, the first layer of taxonomy is just a menu item (thus it's in the url) and the second layer of taxonomy (sub-types) is grouped on the first layer page. For your example, you would click "Computers" and see "Laptops" and "Stationary" as sub-categories. In the "All Products" page that's where the "brand" taxonomy (or the third layer of organization) comes into play.
Using taxonomy would be ideal because "Sony" might produce both laptops and monitors. So a user could go to the "All Products" page and search for Sony to see what kinds of products you offer of the Sony brand.
2) You could build your own "bespoke" solution using Nodes and Menu
If using taxonomy and views and search api sounds too complicated (I'll admit it is a bit intimidating), then you could simply use the Drupal menu system and the Product Displays (the standard Products in Kickstart 2 are actually nodes that reference Products) to build out your catalog.
This video might be helpful: http://drupalize.me/videos/leveraging-menu-system