So, what will you do with the OP verses?
Well, firstly I'd let scripture interpret scripture. So I would need to look at specific cases where leadership is taught in scripture, and also take into consideration the greater narrative of the Bible, and let these help me come to a reasonable interpretation of your three verses quoted. Your three verses are notoriously controversial with theologians and ordinary church folk because they seem so strikingly different, if taken on their own, to what the New Testament teaches elsewhere (and what Paul himself teaches). So in that case, when we're dealing with particularly difficult verses, we must tread carefully and let scripture interpret scripture and, yes, take context into account.
This approach in hermeneutics is not controversial or unordinary. This is certainly a common approach to hermeneutics the world over.
So, with that in mind, we can then see what we can make of your three verses in the OP.
1) The creation order:
A woman should learn in quietness and full submission. I do not permit a woman to teach or to assume authority over a man; she must be quiet. For Adam was formed first, then Eve.
1Tm 2:11
Firstly, we need to make sure that any reference to submission to authority has to also take into account Jesus' own teaching about authority in Matthew 20 and elsewhere. Jesus both teaches, and models, the concept of servant-leadership. God's way is that leaders serve. A president serves his country, his country does not serve him. A CEO serves his team, his team does not serve him. A husband serves his wife, she actually does not serve him - but here is the catch, that she ought to 'submit' to his service. That means that he remains the leader of the household but his leadership is one that serves those he leads (his wife and children). This creates perfect balance - he serves, she submits to his service, and both live in peace and humility before each other. Any man who wants to quote the Bible about submission but does not serve his wife is a hypocrite.
But we ought to ask the question whether submission to men is only in the context of
marriage, which is actually where the concept is most of the time mentioned in the Bible. 1 Timothy 2 seems to expand this submission to church community life, but it also limits it to there. Therefore, woman should be able to lead and teach in other contexts (as they do - note the high volume of school teachers being woman, who seem to fit into this role quite naturally as opposed to men).
So given the limit being imposed here, we can see that 1 Timothy 2:11 in its immediate context has to do with living in peace with each other - and verse 2 is of particular importance, which says we submit to governing authorities "that we may lead a peaceful and quiet life in all godliness and dignity." This points towards living a simple life and watching your ambitions. The rest of the scripture then deals with some examples. It highlights how men should use hands for prayer and not for anger or dispute (verse 8) and talks about how woman should dress modestly and not get involved in the hype of fashion - being concerned with fashions rather than with godliness (verse 9). Incidentally, a lot of modern men should actually heed this scripture as well. There are a lot of men who are so concerned with their looks and their clothes, but aren't concerned with godliness. That's the point that Paul is making, but obviously in the context of Timothy the woman were most guilty of that.
Given this context, we can immediately interpret what it means for woman to be 'quiet' in verse 11 and 12. The Greek word means 'stillness' and 'desistance from bustle'. Paul is reiterating his instruction in verse 2 - to live a quiet life in all godliness and dignity (an instruction given to all in that verse). So ambition and having a big mouth and always having an opinion and being a busybody are obviously the kinds of things Paul is speaking about here. He is speaking about ambition and ego.
So we have a context for submission, which is in the context of servant leadership.
We have a context for 'quietness', which revolves a lot around ambition and ego.
We now need a context for what it means to 'teach'.
I haven't done deep study on these verses, but I can say outright that I find it strange that this does not prohibit a woman from teaching in the church, only from teaching a man in the church. They key, however, is to "have authority" over a man. So the implication I think could certainly be that it means to teach as one with authority. A quick cursory Google search shows much of the discussion is around this word, "authority", and I think it seems to hinge there. A quick glance also, however, indicates that this has to do with
dominating over a man.
If I look at Paul's later statements about Adam and Eve, which you have quoted, I think that's important, and I think Paul is mentioning it not just in and of itself, but is also drawing out the
eschatological implications of the creation narrative. As Adam fell asleep (the Hebrew implies 'dying') and his bride, Eve, was made from his very own body, so Jesus died and his Bride, the Church, is a part of his very own body. This then speaks to
how the Church partners with Christ and how in the same way a husband and wife partner together for God's purposes. Once again, the dying and service is in view - but also a dual partnership in a purpose given by God. It's clear from the creation narrative that Adam was given the purpose of 'tending and keeping' the garden and both Adam and Eve were given the purpose of 'multiplying' and 'taking dominion' of the earth. Eve was created as a helper for the purpose given to Adam, and would be a key part in the taking of dominion etc. Paul is therefore saying the Adam 'came first', meaning, that Eve was a helper in the purpose God gave to Adam. Adam clearly takes a governmental role.
The Greek word
authenteō ("authority") here is incredibly tricky. It appears there are very few cases of this word outside of this text. (This is a cursory glance at the material available that talks about it). If it refers to
dominance, well then, that makes a lot of sense. Given that elsewhere we have already seen that a leader should not lord over or dominate others, but should serve, we could simply say that Paul is saying a woman shouldn't dominate a man, and elsewhere in his teaching he makes it clear a man should not dominate a woman. This would probably be the egalitarian view, or a leading into it.
However, given that Paul goes into the role of overseer in the next chapter, and specifically says the overseer should be the husband of one wife, we could say that it seems Paul does not envisage a wife being an overseer. But the word 'overseer' implies government. So does the word
authenteō (authority) in verse 12. With the creation narrative in view, what we could draw out is that
governmental authority in the church is limited to men, and that is Paul's point. He is not saying women cannot teach, only that they cannot have authority governmentally over men in the church. A very specific
type teaching is in view, and that type of teaching has to do with teaching the overseer(s) of the church - it is
government, not doctrine or theology, that is in view. It is a way of saying that a woman should not dominate over governmental authority in the church. (By the way, this could also be shown in verse 2, given that there government is also in view).
1. A woman therefore can teach and preach and lead numerous other ministries in the church, including apostolic ministry. (Mentioning apostolic ministry opens up another can of worms, but we would have to open up a separate thread for that.)
2. A woman therefore can hold governmental functions elsewhere, but just not in the role of overseer (lead elder / pastor).
3. A woman's submissiveness is to the
government of the church, the overseers, not to every man in the church, and this submissiveness is only in the context of government - in other words, making the final decision on direction and doctrine and discipline in a local church. She is submitted to her husband first, however.
And that's how I would begin to deal with your OP.