Is there a mandate for the types of music during a worship service? Should there be only congregational singing?
There are two scriptures, very similar, that mandate the kind of music for the assembly of the church. “Speaking to yourselves in psalms and hymns and spiritual songs, singing and making melody in your heart to the Lord.” (Ephesians 5:19) “Let the word of Christ dwell in you richly in all wisdom; teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.” (Colossians 3:16)
Any music, regardless of style (classical, pop, rock, rap, etc.) that is either a psalm, a hymn, or a spiritual song (a song about spiritual things) would qualify under these verses. That is good, because if we had to limit our style of music to only what was in existence at the time Paul wrote this, we would be without practically all the songs we use today.
The other part of your question asked whether it must be congregational singing. These verses do not directly state that. They would seem to imply that all or most of our singing should be congregational. Note the essential phrases about what we are doing while singing: speaking to one another, teaching, admonishing. These are actions between people, and since they were written to congregations we may guess that congregational singing was included. Can we exclude choral or solo singing? Not really, as long as the whole congregation participates in listening to what is being taught.
I know of some who insist that singing be only congregational. However, to take that to its ultimate conclusion we would not be able to use songs where part of the congregation sings and the rest (usually the bass and tenor parts) are silent for a few notes, before coming in. Yet from history we know that such antiphonal singing was common in and before the early church. So I don’t think we can mandate only congregational singing. However, we need to avoid a situation where a chorus relieves the congregation from any responsibility for singing.