The monotheistic position on ontology can be summarized by the first few words of the Bible:
Genesis 1:1-2 (ESV)
1 In the beginning, God created the heavens and the earth. 2 The earth was without form and void, and darkness was over the face of the deep. And the Spirit of God was hovering over the face of the waters.
Precisely what this passage means is the subject of much debate. So many books have been written about these words, it's almost impossible to know where to start. (Dietrich Bonhoeffer's Creation and Fall would be my own suggestion.) But what is clear is that God existed "before" anything else and that He created everything. ("The heavens and the earth" was a stock phrase in Hebrew that means "all things", "life, the universe, and everything", "the cosmos", etc.)
Philosophers have struggled with the question of whether God necessarily exists. In other words from a "metaphysical or broadly logical" perspective, can we know that God exists merely from describing His nature? Christians disagree with each other on this point, but all monotheists agree that God does exist, has always existed, and will always exist. Whether or not this may be demonstrated with human reason might be controversial among us, but we all believe that it is true.
Christianity makes a further claim that The Son does exist, has always existed, and will always exist. Here's how Paul phrases it:
Colossians 1:15-20 (ESV)
15 [God's beloved Son] is the image of the invisible God, the firstborn of all creation. 16 For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. 17 And he is before all things, and in him all things hold together. 18 And he is the head of the body, the church. He is the beginning, the firstborn from the dead, that in everything he might be preeminent. 19 For in him all the fullness of God was pleased to dwell, 20 and through him to reconcile to himself all things, whether on earth or in heaven, making peace by the blood of his cross.
Given that statement, we can also reinterpret Genesis 1:2 to include the third member of the Trinity: The Spirit of God does exist, has always existed, and will always exist. The important distinction between Christ and the other members of the Trinity is that He had a body that has a physical existence. It didn't always, but His body does continue to exist and will always exist. (This is what Paul means by "the firstborn from the dead": He is the first person to have a resurrection, eternal body.)
John uses this language:
John 1:1-3 (ESV)
1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was in the beginning with God. 3 All things were made through him, and without him was not any thing made that was made.
John 1:14 (ESV)
14 And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth.
The language in John 1:1-3 is purposefully parallel to the language of Genesis 1:1-2. The Greek word used here is Logos <3056>, which long had a philosophical significance. John is likely applying the ideas of Philo to Jesus in this introduction.
I should point out that the Trinity is an important dividing line for most Christians. Many of the early controversies in the church swirled around the question of just who Jesus was and how he is associated with God. Ontology turns out to be central to Christian philosophy.
Christianity has a strong affinity to platonism with its focus on non-physical Forms. Christians (and other monotheists) believe at the very least that God had a non-physical existence before creation (since the physical world was itself created). But we take sharp exception to Plato's notion of souls. We believe that God created everything outside of Himself, including our souls. Historically, Christians have also taught, contra Plato's idea of transmigration of souls, that the church will experience bodily resurrection and exist for eternity with God:
Revelation 21:3-4 (ESV)
3 And I heard a loud voice from the throne saying, “Behold, the dwelling place of God is with man. He will dwell with them, and they will be his people, and God himself will be with them as their God. 4 He will wipe away every tear from their eyes, and death shall be no more, neither shall there be mourning, nor crying, nor pain anymore, for the former things have passed away.”
God is the eternal, axiomatic, and supreme source of all existence, including both the physical and non-physical.