You have multiple ways to make this work.
What you can do for example, target a page and in the theme for this page or better say the template go and read the GET and make the filtering there.
Another approach and what I personally do is create a page and then start playing with the (add_rewrite_rule) This way I can have clean urls and filter the data in a backend function.
Both ways can give you the flexibility to add more filtering options without big changes.