I believe and our leadership believes Psalms, hymns and spiritual songs include all three categories, so we prefer all three.
I'm glad, at least, that your church includes psalms in worship. It is, after all, commanded. You're part of the way there, which is more than could be said for most churches today. But what do you mean by "all three [categories]"? Would you be prepared to give a definition of each? (I am aware you have already been asked about "spititual songs".)
I ask because, too often in these discussions, people force an interpretation into the biblical texts that cannot belong there. There are two verses in the New Testament that use this formula, "psalms, hymns and spititual songs". They are Col. 3:16 and Eph. 5:19.
Now, what was Paul thinking of as he was writing those words? Was is psalms, man-made hymns, and Hillsong? Now, it has been argued that hymns existed early in the church (some, without justification, even find them in the pages of the New Testament!) but as far as I can see it is not so.
Allow me to digress for a moment and explain my own experience. I grew up in Pentecostal and mildly charismatic churches and I never sang the psalms. The only "church music" I knew was the modern stuff by Chris Tomlin, or the stuff churned out by Hillsong or Jesus Culture (from Bethel Church in Redding).
I moved to Toronto, where I started going to a liberal Presbyterian church. They had an organ and, along with modern worship songs, they sang hymns. I had never experienced the like. I remember the first hymn I sang in church was "Crown Him with Many Crowns". My heart swelled (along with that organ) like never before. I developed a love for hymns and set out to memorize them, as, I thought, I had been deprived of my Christian heritage! (I still sang and loved many modern songs as well.) I have since gone through difficult times and have found some hymns to be a great comfort to me. I have wept singing "Amazing Grace" reflecting on God's goodness to me.
Now, some years later, I will not sing hymns or modern worship songs. (I might occasionally hum the former or play the tunes on the harmonica.) I did not arrive at this position easily. My love of man-made songs in worship was, in the end, defeated by Scripture. I know now that the organ, as well as other instrumentation, is used manipulatively and my enthusiasm was in part generated by it. And I know now that God commands no man-made songs. And I'm happier for it. For one thing, no longer must I test all the words that I sing. I know them to be true. And I know that I am singing with Christ, my Lord and God.
Modern Christians have a love of hymns and worship songs. A love of the psalms is certainly lacking. As I've said, I'm glad your church sings psalms. It's better than nothing; hopefully it gets the Lord's people to appreciate them more.
But let me be plain: "psalms, hymns and spiritual songs" do not refer to modern categories. That is simply an anachronism forced on the texts by modern readers. "Psalms", "hymns" and "songs" are all headings in the Septuagint psalms. (The word "spiritual" means "of the Spirit" and can in these verses be taken to apply to all three categories.) Ask yourself: What would a first-century Greek-speaking Jewish or Gentile Christian think upon reading these words in a letter from Paul? (I can tell you it's not "Oceans".)
We sing Psalms and hymns every Lord's Day. As well, a lot of the hymns are based on the Psalms. In my opinion, they are all a blessing and to be preferred as long as the content is biblical and truthful.
Some hymns and worship songs are very nice, but that's not an argument for their inclusion in worship. At least not according to the Regulative Principle. I can't let my preferences to get in the way of God's worship.
My worship must conform to God's command.
Sola Scriptura. If my doctrine or practice does not line up with what the Bible says, I need to stop and think carefully and payerfully.
Our pastor once preached on this and summed it up as spiritual songs fitting into the category of taking Scripture and making a song of it, like singing Mary's song or another portion of the Bible. Also, a song like How Firm a Foundation, it's taking a portion of Isaiah and setting it to music.
I can sort of appreciate the effort your pastor's going to, but let's be straightforward: there is no such command in Scripture. Moreover, isn't he just reading a modern view into the text? Again, what would a first-century audience have understood by that word "songs"?