This might be helpful: https://ggullentops.blogspot.com/2018/07/sitecore-sxa-search-overview-pages.html
Adding the filter to the page is not that hard - it's a standard component. Getting the facet that is used by the filter component right is a bit more tricky.
If you want to have a facet on a single line text you should use a
List Facet. Create your facet in the facets folder "Tenant/Site/Settings/Facets/" and set the
Field Name. This has to be the lowercase name of the index field that is used for the facet (your product type). Check your index to get the correct name...
Next step: go to "Tenant/Site/Data/Search/Checklist Filter" and create a new Checklist filter. Select your facet and adapt texts as needed.
This filter item will be the datasource for the Checklist component that you can put on your page.