Our church has a consistent order of service: music to get people into the sanctuary, a song to start, a prayer, a song set, perhaps a testimony, preaching, maybe the Lord's Supper, then a song set and closing prayer. The band (aka “worship team”) sings and plays, and if the drums are loud or the sound man is easily influenced it gets hard to hear the congregation. The focus is pretty much entirely on the stage. There's no “invitation” as such beyond a suggestion that people visit either the Welcome Banner or the Prayer Banner areas (the latter is a very good feature—people stand ready to pray with anybody needing prayer).
You may think my description is less than enthusiastic. I've been in much worse services. And better.
Baptists point out that all Christians are part of the “royal priesthood.” The ordinary Christian enjoys the right and responsibility of direct communion with God, with no intermediary. If we take this seriously, it further means that the Christian can be an intermediary for the non-believers, able to intercede on their behalf.
So imagine a congregation of priests. If you want to lead them in worship, do you sing at them and talk at them and keep them passive, or do you involve them?
I don't have a clear picture yet, or clear answers, but it would seem a hugely wasted opportunity if you did not invite those priests to pray together, to recite scripture together, to call on God together, to sing together, to pronounce blessings together.
Praying together can be silent, or assenting to the prayer of a leader, or praying out loud together. Having someone from the congregation pray seems fitting also. As it is we generally only allow the assent to the leader's prayer. There's no accommodation for silent prayer at all, unfortunately.
Singing together with a focus on the congregation is almost the opposite of the almost passive audience we get with the stage band and powerpoint slides. I suspect that only a small fraction of the congregation know how to read music anymore. I've been in a few churches where the speaker amplifier was mistaken for the power of God—and the louder the better.
I've never found any convincing reasons why the Lord's Supper should not be offered each service, although that's not strictly part of the theme here.
Even Pentecostal services have an order, and it seems better to recognize that a worship service is going to have an order and try to make it as fitting s possible.
Announcements and such non-worship activities should be outside the boundaries of the order of service. It has been a wise tradition to open the service proper with an invocation remembering Jesus' promise of his presence, and to close it with a prayer and a blessing. Within those boundaries everything should be ordered to praise and edification and the practice of the presence of God. Were it my choice I'd forbid applause on the grounds that this time should be focused on God alone.
I'm reluctant to try to specify a particular order, but the general shape should involve communal prayer, communal scripture, silent prayer, singing, blessing, preaching, and the Lord's Supper. There's a dramatic logic to some of the traditional orders of service, which might be usefully revisited, though some of them are extremely leader-centric.
It's been implicit—let me make it explicit. The worship service is not principally for evangelism, but for worship. Imagine that I am a “seeker.” If I go to a Buddhist service I want to see what Buddhists do, not sit through a lecture explaining that I ought to be one myself. I can figure that part out after I find out what they do.
I'm still thinking about this topic. I think there's room for lots of flexibility, and in a small church even room for unexpected changes. But if a core principle is that the congregation is active, then you can't keep assigning them the rather passive role our church generally does.