[what's up]

Now, is it logical that God, the Almighty Father, would select a woman as a vessel for the Incarnation who was tainted with sin, and under the influence of Satan?

We don't have any indication that Mary was under the influence of Satan. She accepted the Word of God given her by the angel. Why would you say that was influenced by Satan? She likely walked by faith as did all God's servants.

But even though she had faith she was still a fallen human. God uses fallen humans for all kinds of things. He is God. He is able.

[JCBreckenridge]

And he’s also able to keep her free from sin entirely.