By default , you already have different ways to display the categories of products and their associated products in HikaShop.
You have two possibilities in order to display your categories of products : use the module "Categories listing on 2/1 levels" or use the menu item "Hikashop categories listing".
Display in Div
Display in List
First of all, create one or several categories and sub-categorie which contain products, in the "Categories" manager of HikaShop.
Then, go in the Modules manager of Joomla. and enable the "Categories on 2 levels" HikaShop content module. You can also choose the categories you want to display and how to display them via the HikaShop options of the module, or select a position where to display the module on your template.
Go in the Menu manager of Joomla.
Move the HikaShop "Categories listing" menu item from the HikaShop default menus to the main menu. Then, you can play with the HikaShop options of the menu item ! Choose the categories that you want to display and how.
Go in the "Display" tab of the Hikashop backend configuration page.
(Hikashop / Configuration / Display) and manage the general display options of HikaShop.