Baptism - how should it be done?

As far as baptism versus sprinkling, during a discussion of this very topic, I came across this account:
"Asfaw was a student in [a] missionary training school. After graduation, he went to the Borana people. He began a sports outreach that brought many to faith in Christ, but there was no water deep enough for baptism and it rains only once or twice a year there. So Asfaw dug a hole ignoring the taunts of the community, then he prayed and fasted, and God sent enough rain to fill the hole, time after time. Pray for Asfaw as he pastors the church he planted, and for the new Bible School the Kale Heywet Church has established to train leaders for the emerging Borana church." (SIM Magazine)
So God does honor those who seek to do his will, in all they believe he requires of them. Also, the word "baptize" really does seem to mean submersion in water, although surely no one would insist that a person who for medical reasons could not be immersed, could not be sprinkled with water instead. Nor would it seem that those who were sprinkled must be subsequently immersed!
But immersion is very similar to Paul's description of what baptism represents, while sprinkling is not, so it would seem that immersion, if possible (and sometimes if impossible! as above) would be best.
But what words should be used? Some teach that "in the name of Jesus" is correct, yet others (notably, the Baptists!) teach that "in the name of the Father, Son and Holy Spirit is correct. Now first, this verse should be mentioned:
1 Cor. 1:15 ... so no one can say that you were baptized into my name.
This seems to show that "baptize into the name" does not refer to the words used in the baptismal ceremony, Paul would not have said "I baptize you in the name of Paul"! I think it safe to say that none of the Corinthians would have thought this. So "baptize into my name" must mean to baptize as a follower of the one who was named, not the actual words used in the ceremony.
But Acts 8:16 may indicate an error on the part of those who baptized the converts:
Acts 8:16 ... the Holy Spirit had not yet come upon any of them; they had simply been baptized into the name of the Lord Jesus.
Now I would not expect that this means the baptismal formula was wrong, but instead, that these converts were aware only of Jesus and their teaching had been lacking, not the formula. When they declared their allegiance, it may well have been only to the Son, and not the Father or the Spirit. Note that they were not rebaptized! Instead, Paul and his companions prayed for them, and they received the Spirit.
But what formula should be used? I think it would certainly be important for what is said to mention the Father, Son and Holy Spirit, especially since some hold that only the name of Jesus should be used, endorsing a belief that there is only one person in the godhead. Yet I would say an even more critical aspect in this regard would be a conscious allegiance to all three members of the Trinity, not simply a mention of them, at the time of declaring an intent to follow Christ.