According to Protestantism why did God choose the persona of a Father? Throughout the Bible, God uses the persona of a Father.  Jesus specifically refers to God as Father, and us as his sons.  Why is it significant that God is a Father? And why did God choose the nature of Father to commonly describe his character, as opposed to other relationships that God created, such as that of Mother or a non-descript purely spiritual nature?

How is this viewed in general Protestant traditions? And are their significant variances across these traditions?
As is pointed out in the comments, the question tends to put the cart before the horse.  God established the institution of "father".  The Old Testament represents God by many different names, each one expressing a different aspect of who God is (i.e. El Shaddai-Lord God Almighty, Jehovah Jireh-The Lord Will Provide, etc.)  God is represented as Father in the New Testament, not inconsistent with His OT character.  The difference comes with the intimacy of the term consistent with the intimacy established by the New Covenant.  Paul stated, "the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.But after that faith is come, we are no longer under a schoolmaster. (Gal. 3:24,25). The transition from law to faith is paralleled by the transition from "Adonai-Lord, Master" to "Father".  The tearing of the curtain separating the Holy Place from all but the High Priest and then only once a year is yet another illustration of this revelation that God is not only "El Elyon (The Most High God)", but also "Father", a figure of authority who is capable of and expected to love us.  Likewise, Christ's designation as "Son" illustrates someone with whom we can identify and helps us to understand, as Paul puts it, "...our adoption to sonship..." (Rom. 8:23)  Our ability to understand God is limited at best and nobody understands that better than our Creator.  Loving Father is how He wants us to know him.