The most effective way I have seen with a church choir is a prepared director. Like jonathan said that knows every part. The old MOM at my church was effective. He would teach one section their part then 2 sections would sing together then 3 part harmony.
Really you could teach the soprano and baritone their part at the same time if you want. They are usually going to be the same although he used to teach baritone/bass with the tenors.
But he might teach the soprano their part until they got it, Then he would sing the alto part with the sopranos. Then altos and sopranos would sing together. By this time the tenors pretty much had their part. But then he would have all three parts sing. This was the most time efficient for our church.
He would use that method or he would start with tenors then do tenor/alto and then tenor/alto/soprano.
Me personally though when I get my time. I would train the choir in music exercises that teach them range, pitch, and harmony. Then I would use the method 1 part, 2 part, 3 part,.... harmony.
I have seen directress's waste alot of time teaching one part then teaching the next part then the next. By the time they all get harmony the sopranos are singing the alto part and the altos are singing tenor. I think its better having harmony going on with teaching parts because it teaches the choir to hear harmony. If if it doesnt work for you try something else.
With the choir learning songs I say they should have atleast two rehearsals before singing a song so that means you must be prepared. If the song is long then its cool to break it up. If its just a regular church song then I say go through the whole song. Then clean the song up in the next rehearsal.
This is the setup for choir rehearsal at my church but Im just a musician. If i was leading I would change things up.
30min prayer
Scripture
Devotional song
Business
Warm up song
Rehearsal
Usually we waste alot of time doing this. lol It takes 20 mins to decide what they are going to wear. Dont do that.
This is what I would do.
Musicians Rehearsal
Work with solo vocalists before actual rehearsal.
Special needs vocalists. lol
Rehersal
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Prayer...whether kneeling or holding hands
Scripture
Vocal warm up exercises and technique
Hymns
New Songs 10-15 mins per song
Sunday morning line up
If you seriously want to learn 4 part harmony a hymn book is the easiest way to go. Our church sings 2-3 main songs every Sunday. The rest of the songs are the same. This means I would have 6 main songs every rehearsal. 3 would be from the previous week and the next 3 would be new. I would go over the Sunday morning line up to make sure the new and old members have all songs down. Maybe even march in. Some people find this boring but excellence requires you be thorough. I personally think if you did these things every rehearsal you would have a well trained choir. I would even bring in guess directors and musicians from time to time to share with the choir.