Make search page with Taxonomy
to reduce results by the content type, when you set up the view, filter by content-type, and select the appropriate content type. If it already exists, use a FILTER CRITERIA and use content-type (I believe this can also be accomplished through the search settings)
to group: set format to fields, add the taxonomy term to the fields list to group by (you can hide from display if desired), click on Settings under FORMAT. There you can group by any field currently in the view
for Solr, take a look at Apache Solr Views Module and the related documentation for implementing this functionality.


Apache Solr Views:


  This module provides a Views integration to the Apache Solr Search
  Integration project. It provides the views plugins and handlers needed
  to be able to create a view that fetches its results from Apachesolr
  index, without hitting the database.