Prestashop "Sort products by -> xxx"

i've searched the web for quiet some time now. I'm currently in the making of a webshop in prestashop, trying to make a filter which can sort products by different categories.

I want the users to be able to sort the products in the products(view/list) by some different categories as;

Product type (Random names)

Lamp heads (1, 2, 3)

Lamp head corners (four, six, etc)

I want this to work just as product attributes does, in which you can use the radio-buttons to specify what product you are looking for.

Which means, i want people to be able to sort the view by, a specific product type (Amalie) with 1 lamp head, and six head corners. (When they do so, i want the customers to be able to see every product that contains these values).

What i've tried:

Using categories -> Problem here is that if i sort by categories, i cannot name the categories + attributes, you do one of those, not both.

Using attributes -> Problem here is that if a customer gets by the sorting with attributes, they will be forced to pick the attributes again (1 lamp head, amalie, six corners) on the product site + i will have to specify the product price again because of the "variant" of the product.

So.. TL:DR;

I need a module/piece of code/a guide, to be able to sort my products by specific type, lamp heads & head corners. Without getting forced to a new page, and without having the customer pick the variant of the product more than once, + me having to name the specific price of that variant.

If all this doens't make sense, feel free to ask me again! I tried to specify my request the best i could.