Mary is the Mother of God only in that she is the mother of Jesus.
As many have agreed, Mary does not precede either the 1st, 2nd, or 3rd persons of the Trinity, nor did she give rise to the eternal Godhead.
Then she should have been called "Christotokos" as Nestorus suggested, or perhaps as "Iesutokos," but the church resolutely rejected that (I believe only thee bishops of 150 or so) voted for Christotokos. I suggest you read the whole text of the Council in order to get their reasoning on this one.
Of course, the implication is that she is not someone who preceded either Person of the Holy Trinity.
Personally, my approach to orthodoxy is defined by Leo Tolstoy's Three Little Hermits. I am perfectly comfortable just praising in humility and awe the Tiune God and letting Him guide my heart, even if I don't know how to serve Him, or how to "officially" pray to Him.