How to display both categories and tags on a product landing page

I'm using the Marta template (Brine family). Part of the purpose of my website is to sell photography prints. I've been using categories to sort my pictures into different groups. With the Marta template, the categories automatically compile on the side of the page, which is good. But I would like to also display my tags on the same page.

My ultimate goal is to be able to allow the user to select the orientation they would like their picture to be. The categories list is sorted alphabetically so "Vertical" and "Horizontal" wouldn't be next to each other in the list. Another way my goal could be achieved is if there was a way to format the categories list to customize the order that the it's displayed.

My product landing page for reference

Can you explain a little more about why you need tags? Is this for filtering purposes?

I don't necessarily need tags, what I want is a separate list of filtering links. I'd like to allow the user to choose what kind of orientation they would like and then the category.

So for example I'd like for them to be able to select "horizontal/landscape" and then choose the category that they want.

I'm really not sure if it's possible to select a category and a tag at the same time since I can't even view my tags.

You can filter by tags and categories using links, but some use cases are easier to achieve than others. For example:

You can filter by a category and a tag, showing only results that meet BOTH requirements (those that are of the category AND of the tag).

You cannot filter by multiple categories, showing ONLY those that meet ALL the categories.

You cannot filter by multiple tags, showing ONLY those that meet ALL the tags.

There's a plugin available that makes this much easier: Universal Filter.