The Bible doesn't explicitly state a single "ultimate goal [of living a life]," but it gives plenty of suggestions on how to live, as the question states. It seems reasonable to infer that the guidance in scripture reflects the view of the God who (according to the scripture) inspired it.
When Christ was asked which was the greatest commandment (Matthew 22:35-40), he drew his response from the Jewish scriptures:
"You shall love the Lord your God with all your heart and with all your soul and with all your mind. This is the great and first commandment. And a second is like it: You shall love your neighbor as yourself. On these two commandments depend all the Law and the Prophets."
John's gospel (John 10:10) quotes Christ as saying:
I am come that they [the people] might have life, and that they might
have it more abundantly
...so perhaps to love God, love your fellow humans, and live life to the full.
John's gospel (John 3:16) also quotes Christ as saying,
For God so loved the world [kosmos], that he gave his only Son, that
whoever believes in him should not perish but have eternal life"
...pointing to an eternal dimension to this life.
This is supported by Luke's gospel's account of Christ, telling a thief who was being executed alongside him, "today you will be with me in paradise." (Luke 23:43).
The New Testament letter to the Hebrews additionally speaks of death followed by judgment: "people are destined to die once, and after that to face judgment." (Hebrews 9:27). There are a number of views as to exactly how we are judged. Christ, in Matthew's gospel (Matthew 7:21-23), says:
Not everyone who says to me, "Lord, Lord," will enter the kingdom of
heaven, but only the one who does the will of my Father in heaven. On
that day many will say to me, "Lord, Lord, did we not prophesy in your
name, and cast out demons in your name, and do many deeds of power in
your name?" Then I will declare to them, "I never knew you; go away
from me, you evildoers."
It seems clear that heaven, or paradise, is a state to be desired in an afterlife. Less happy states are available - "being in torment" and "lake of fire" are mentioned, though not "devils with pitchforks" interestingly enough.
The Jewish prophets also had plenty to say about what God wants from us (it being always assumed that our purpose includes doing what God wants).
An example: "What does the Lord require of you but to do justice, and to love kindness, and to walk humbly with your God?" (Micah 6:8) - which includes action, inner attitude, and relation to God.
In addition to living well, we are called to praise God: for example "Sing to the Lord a new song, his praise from the end of the earth!" (Isaiah 42:10).
In general the prophets seemed more concerned with how we live now, and how we relate to God, than with exactly what happens after we die.
"Unifying with god," in the sense of becoming part of or merging with God is "not a thing" in scripture, although likeness to or imitation of Christ (or God), presence and fellowship with God, and following his will and law, are themes, as is glorifying and worshiping him.
As to what is heaven - we don't have a lot of detail, and anything we do know (finite as we are) must be more like a metaphor than a prospectus.
But Jewish and Christian scriptures speak of "a new heaven and a new earth" (Isaiah 65:17, 2 Peter 3:13, Revelation 21:1), and of resurrection - the Apostle Paul says, "I have the same hope in God as these men themselves have, that there will be a resurrection of both the righteous and the wicked." (Acts 24:15). The Christian Church broadly understands this as a bodily resurrection - as the Nicene creed puts it, "We look for the resurrection of the dead, and the life of the world to come."
Thus the end state is seen as a continuation of individual existence, and a worshipping relationship with the Divine, rather than a merging into some sort of divine essence or an end to the burden of experience.
One summary I quite liked is that our purpose here on Earth (as individuals and as a community of believers) is to show God's glory to the world. Simeon, when Christ was brought as a baby to the temple to be circumcised, said "mine eyes have seen thy salvation... a light to lighten the Gentiles, and the glory of thy people Israel." (Luke 2:30,32). Christ said, "let your light shine before others, that they may see your good deeds and glorify your Father in heaven." (Matthew 5:16)
The Presbyterian formulation of "to glorify God, and to enjoy him for ever" is fine, as far as it goes, as a summary of the eternal state, but for me it concentrates too much on "what's in it for us" and not enough on the journey - and the gospels and the Jewish scriptures are very much about the journey.