These are brief: one tidbit each from the Hebrew Bible, the writings of the New Testament, and from the history of Churches of Christ.
Miriam was both a prophet (Exodus 15:20) and a leader (Micah 6:4). She was one of the three people (along with Moses and Aaron) God sent to lead Israel out of Egypt and through the wilderness (Micah 6:4). In addition, she served another role as well: worship leader.
Once Israel crossed the sea and the Egyptian army was destroyed, Miriam took her tambourine and, with other women, played and danced before the Lord. And “Miriam,” the Bible says, “sang to them.”
Our English translations do not typically specify to whom the “them” refers. Most English readers, in my experience, presume it refers to the women. But the Hebrew text is clear: “them” is masculine. Miriam sang to the men (probably the whole congregation). In other words, Miriam led Israel’s first communal worship after the Exodus. Israel’s first worship leader was a woman!
Eve is only named in two passages in the New Testament: 2 Corinthians 11:3 and 1 Timothy 2:13-14. In both passages Eve is mentioned because she was deceived.
Because Eve was deceived, some have thought women are more easily deceived, perhaps (they say) due to their supposed emotional nature, natural instability, or weaker mind. But Paul offers no reason for why Eve was deceived; male interpreters have invented these dubious rationales. In my experience men are deceived as often as women. In fact, the Bible regularly warns everyone about deception (e.g., Ephesians 5:6). Further, we might even say, Adam was weaker because he ate the fruit even though he was not deceived.
Paul uses Eve as a typology of deceived people. In 2 Corinthians 11:3 whole groups of people (men and women) were deceived like Eve. In 1 Timothy 2:13-14, Eve represents the women in the Ephesian congregation who had been deceived by false teachers. She illustrates the danger present when deceived women lead or teach. That same danger is true for men as well, but the specific situation in Ephesus involved deceived women—some had already been captured by Satan (1 Timothy 5:15). Paul is neither describing every woman nor the nature of women but identifying one woman from the Biblical story who was deceived in order to highlight the local problem in Ephesus. It is not a universal statement about women.
Daniel Sommer (1850-1940) was a leader in the conservative wing of the Churches of Christ. In fact, some believe he was the major force in the division of Churches of Christ from the Christian Church through his participation in the Sand Creek Address and Declaration in 1889. Those congregations announced their separation from other congregations who practiced “innovations and corruptions.”
At the same time, Sommer advocated for the “privileges” of women to participate in the public worship assemblies of the church. Though he was not egalitarian (e.g., he did not believe they should preach or rule (elders in the church), he encouraged women to lead prayer and read Scripture in the public assembly. Moreover, he encouraged women to “exhort” the congregation in the public assembly. “If a sister in good standing,” he wrote, “wish to arise in the congregation and offer an exhortation it is her privilege to do” (Octographic Review 44.34  1). Apparently, such a practice was not an innovation. Typically, Churches of Christ do not permit any audible participation of women in the public assembly except singing and their good confession at baptism (or perhaps the occasional “amen”), but it has not always been so among us.