As said in the documentation:
Must: The clause (query) must appear in matching documents.
Should: The clause (query) should appear in the matching document. In a boolean query with no must clauses, one or more should clauses must match a document. The minimum number of should clauses to match can be set using the minimum_should_match parameter.
In other words, results will have to be matched by all the queries present in the must clause ( or match at least one of the should clauses if there is no must clause.
Since you want your results to satisfy all the queries, you should use must.
You can indeed use filters inside a boolean query.