First, the caveat: I confess the Athanasian Creed. I believe that in this Trinity none is greater or less than another.
And yet I also note that Scripture is very clear about the Monarchy of the Father - one thinks of 1 Cor. 15 among other passages.
What I have found striking is this: the Son prays, for He lives to intercede for us. The Spirit prays for us with groans to deep for words. To whom do they pray if not to the person of the Father? But Scripture nowhere depicts the Father as praying; the very notion makes no sense. He is the recipient of all prayer: both ours and the prayers raised by the Second and Third Persons of the Blessed Trinity.
Thus one is struck with how the Church quite naturally prays to the Father in the liturgy - overwhelmingly so. Not that there is not historic prayer to the Son (the "stir up" collects of Advent) or to a lesser extent to the Holy Spirit (the frequent plea for Him to "come" in the hymns for Pentecost) or even naming all three persons (the collect for this coming Sunday), but that these others have nowhere near the frequency of our liturgical prayers addressed to the Father.
In this the Church's prayer confesses the order of our salvation, for it was the Father who sent the Son into the flesh and it was the Son who sent the Spirit from the Father who brings us to the Son to receive His gifts that He might at last present us to the Father. The Father is thus source and goal, and we are then given the shocking and glorious insight that we are being invited into is nothing less than the inner-life of the Trinity, that our prayer be offered through the Son and in the Spirit (and thus with the Second and Third Persons) to the Father.