In this blog, I'll list out the REST API URL to retrive the list collection based on the List template.
 
To retrive all lsist and libraries from the site

https://sharepointsite/subsite/_api/web/lists

Following examples show you how to retrieve the  list / librarues based on the template type,
Syntax

 https://sharepointsite/_api/web/lists?$filter=BaseTemplate eq <Template Id>
 
Examples:

To retrieve the collection of Document Libraries

https://sharepointsite/subsite/_api/web/lists?$filter=BaseTemplate%20eq%20101

To retrieve the collection of custom Lists

https://sharepointsite/subsite/_api/web/lists?$filter=BaseTemplate%20eq%20100

To retrieve User Information List
https://sharepointsite/subsite/_api/web/lists?$filter=BaseTemplate%20eq%20112

This link has the id for List template types.

To retrieve only the hidden list / libraries,

https://sharepointsite/subsite/_api/web/lists?$filter=Hidden%20eq%20true
 
Exploring SharePoint REST API...