So, why and when should we sing in worship? I suppose there's no theological reason why the whole worship service couldn't be sung. Sermons in plainsong, anyone? It seems the further east one goes, the more of the service get sung. Take, for instance, the many fine Coptic websites dedicated to improving liturgical hymnody, by which they mean something more comprehensive than what we mean by the term in Western Protestantism. I was swooning at the singing of St. John's Passion at an Episcopal church I visited at Good Friday. (Though the words were the same, the singing made the anger of "crucify him" turn to pathos, and made the whole narrative seem less anti-Jewish. This helped me just be there and thus kept it deep, without the now de rigueur sermon about how it wasn't the Jews' fault. Can't the sermon just be about the cross, the sacrifice, and the salvation of the world? OK, back to the point.)
Of course, by the time you get to the wading end of the liturgical pool, which the Unitarian Universalists share with most mainline Protestants, the hymns often have one function (to stir to a purposeful action) and the quasi-service music has another (to soothe or inspire). Praising God isn't at the top of the list; neither is entering a rythmic meditative state that uses words but defies the verbal to enter into closer relationship with God. No, wait: maybe the latter one is on the cards. You can almost see it happening with a congregational rendition of Spirit of Life (which I detest with a passion) or Come, Come Whoever You Are, but I doubt anyone but the Pagans sense what great thing is on the verge of happening. That's why they bring the drums.
But when you ask, "why the first hymn?" you have to ask "why the sentences (or opening words)?" because their function seems intertwined. Ditto for the psalmody (or responsive reading) and the middle hymn or choral selection, where these exist. And what about a hymn before or after the sermon, or both? Indeed, the whole criticism of the "hymn sandwich" approach to low Protestant worship is because there doesn't seem to be any real reason why we do what we do. It isn't enough to side (even sarcastically) with the most conservative Calvinists and say that it was a mistake to introduce human-crafted hymns in place of God's own psalms (a funny argument itself) because hymn composition reaches back to antiquity at least, and hymnic fragments seem to litter the letters of the New Testament itself.
The congregation and its deputation, the choir, has music to sing; indeed, this is a key part of the traditional lay role in worship, and so why reduce that role? Time to hit my old hymnody textbooks for threads to follow to asnwer the questions: why do we sing what we sing, and where we sing them?