Craft Commerce - Product Types URL
Probably the most Craft-y way would be to use categories for classification and set your categories to have URLs.

Alternatively, you could do this with a route that points shop/* (ie. shop/{some token} - at a template, say shop/product_type and in that template use the second segment of the url in retrieving products of the appropriate type (or, of course, create 3 routes and 3 templates if they way you're handling those index pages differs a lot).

In general how Craft deals with routes/urls is documented here:
https://craftcms.com/docs/routing
And some more info on routes is here:
https://straightupcraft.com/events/routes-and-patterns

Then to create your menu/list or whatever, something like:

{% for productType in craft.commerce.productTypes %}
  &lt;a href="/shop/{{ productType.handle }}"{{ productType.name }}&lt;/a&gt;&lt;br&gt;
{% endfor %}


(on phone so excuse any syntax errors)