To determine the meaning of a term which is unusual and somewhat difficult, one really needs to take all relevant Scripture into account before arriving at a sound interpretation.
1. The Bible already reveals very clearly that Jesus - the eternal Word of God -- is the Creator of the universe (Jn 1:1 and others).
2. The Bible already reveals that He is God (1 Tim 3:16 and others), also called the Son of God, the Son of Man, and with many other titles and designations.
3. With reference to the Son of God, Jesus is "the only begotten Son of God" and that needs to be taken into account.
4. So now we must see what that word "firstborn" means, firstly in its lexical sense, and secondly in its theological sense.
Who is the image of the invisible God, the firstborn (Gk prototokos = firstborn) of every creature. (KJB) In this instance, the NLT paraphrase actually explains the meaning about as well as any other interpretation: Christ is the visible image of the invisible God. He existed before anything was created and is supreme over all creation.
Since "firstborn" pertains to birth, and "only begotten" pertains to "begetting" or birth, we need to tie these together. Unfortunately, modern versions have expunged "only begotten" from their translations, but it is right there in the Greek as monogenes, which means "uniquely begotten".
Jesus -- the eternal Word -- was with the Father and the Spirit from eternity past. There is no mother involved, and all the Persons of the Godhead are masculine. Therefore there can be no comparison to human begetting. So in what sense was Jesus "begotten", which makes Him "the firstborn"? The only proper way to interpret this is that a UNIQUE Father-Son relationship has existed within the Godhead from all eternity. This does not diminish the deity of Christ in the least, but shows us how He is the firstborn of all creation. The Creator is also the only (or uniquely) begotten Son of God, and has primacy over every creature and all creation.
I also believe Jesus to be The Word, but what I mean by that is that I believe The Only-Begotten Son of God to be the Word, not God. We must understand that when it comes to mankind, man begets by procreating God begets by creating. While I agree that God and his Only-Begotten Son has a unique Father-Son relationship, I disagree that Gods Only-begotten son had no beginning, God alone is the only person who has no beginning, no one else is like him in that respect. We can't say exactly when this unique Father-Son relationship began since we know not when God brought his only begotten Son into existence.
Monogenes which as you say means uniquely begotten has to be considered in how the scriptures use this term. Considering Isaac the son of Abraham was the only-begotten son of Abraham, yet Abraham had another older son that he beget who was Ishmael. That doesn't mean Isaac wasn't the only begotten son of Abraham because as you said Monogenes means uniquely begotten. How was Isaac uniquely begotten, well he was the only son of promise, he was the only son by Sarah and the only Son left with Abraham when Abraham died.
The apostle John repeatedly describes the Lord Jesus Christ as the only-begotten Son of God. (
Joh 1:14; 3:16, 18; 1Jo 4:9) This is not in reference to his human birth or to him as just the
man Jesus. As the
Loʹgos, or Word, “this one was in the beginning with God,” even “before the world was.” (
Joh 1:1, 2; 17:5, 24) At that time while in his prehuman state of existence, he is described as the “only-begotten Son” whom his Father sent “into the world.” —
1Jo 4:9.
He is described as having “a glory such as belongs to an only-begotten son from a father,” the one residing “in the bosom position with the Father.” (
Joh 1:14, 18) It is hard to think of a closer, more confidential, or more loving and tender relationship between a father and his son than this. —See
BOSOM POSITION.
The angels of heaven are sons of God even as Adam was a “son of God.” (
Ge 6:2; Job 1:6; 38:7; Lu 3:38) But the
Loʹgos, later called Jesus, is “the
only-begotten Son of God.” (
Joh 3:18) He is the only one of his kind, the only one whom God himself created directly without the agency or cooperation of any creature. He is the only one whom God his Father used in bringing into existence all other creatures. He is the firstborn and chief one among all other angels (
Col 1:15, 16; Heb 1:5, 6), which angels the Scriptures call “godlike ones” or “gods.” (
Ps 8:4, 5) Therefore, according to some of the oldest and best manuscripts, the Lord Jesus Christ is properly described as “the only-begotten god [Gr.,
mo·no·ge·nesʹ the·osʹ].” —
Joh 1:18,
NW, Ro, Sp.
A few translations, in support of the Trinitarian “God the Son” concept, would invert the phrase
mo·no·ge·nesʹ the·osʹ and render it as “God only begotten.” But W. J. Hickie in his
Greek-English Lexicon to the New Testament (1956, p. 123) says it is hard to see why these translators render
mo·no·ge·nesʹ hui·osʹ as “the only begotten Son,” but at the same time translate
mo·no·ge·nesʹ the·osʹ as “God only begotten.”