A foundational principle of hermeneutics is to read the scriptures un-anachronistically, that is we shouldn’t import our 2lst Century meanings into the text. To do so is a form of (unintentional) eisegesis.
What do Jesus, James, and Paul mean when the refer to “hymns” and “songs”? We think we know what they mean when they refer to “psalms”, but what are they referring to with “hymns” and “songs”?
My Pastor addressed this issue on Lord’s Day 31 with his message from Mark 26-31. I have posted the relevant portion above, approximately 14:30.
This issue of what we sing in worship to our God has to do with the Regulative Principle of Worship. This is not an issue of what we sing during the regular activities of the day, but what should we sing in worship to our God.
Resources I would recommend are ExclusivePsalmody.com and John Brown of Haddington’s Introduction to his Psalms of David in Metre.
Finally I should note that there are two groups and sub-groups within Exclusive Psalmody advocates. There are those who advocate singing directly from the Psalms in your bible translation and those who are fine with singing from the psalms transcribed in metre. Two sub-groups within these two groups are those who advocate singing a capella and those who are fine with instruments. (I’m sure that within the instruments group are further sub-groups of which instruments are and aren’t allowed in worship - such as, organ but no piano; piano but no guitar; acoustic guitar but not drums, etc.)