Best Plug In to develop a search/result widget?

Hi,
I’m trying to make a database searchable in a widget on a particular page for my website. It’s sorting degrees by level and specialization and credits.
I tried using customizing product filters and WooCommerce “finder” widgets — but they all require a “buy” feature. I just want the user to be able to select:
– degree type
– specialization
and have the results filtered accordingly. Something like this would be awesome! http://www.uidaho.edu/degree-finder
I feel like this should be easy by using a custom field database search widget but I’m having trouble locating one that works.

Any suggestions? Thank you!