I think you’d be missing out on a lot of the color and depth of Christianity but otherwise you should always do what you feel is right.
The NT is the coda to a long story that begins with the creation (genesis) of mankind. The story is one of mankind’s struggle to master the world and himself. The sad reality is that humans are flawed. Understanding the story the whole Bible tells gives you crucial insight into how those flaws manifest.
Adam and Eve shows us that even when given the whole world, lives of utter perfection, no struggle and strife ever, we manage to throw it away like a moldy sack of potatoes.
God can do tremendous things for us, like cause the very seas to part so that we can escape a pursuing army, and we’d still forget and disobey and question and reject God. He can give us the most perfect king imaginable, with his descendants numerous, and still we will find our way back to wickedness and iniquity.
The New Testament is as close to real history as it gets in the Bible. The efforts of Paul and the other evangelists to build an enduring church to keep the teachings of Jesus alive is compelling reading.
Nothing God did before giving us Jesus actually worked. We always managed to forget God, forget this magical divine way of existing in the world. Why did Jesus succeed where David failed? That’s the story the New Testament tells. It’s all there.
David’s was a temporal kingdom, one that would have fallen to the Romans had it lasted that long. Jesus’s is an eternal kingdom that can morph into anything its called upon to do, fit into and around any temporal nation. These things didn’t just happen, people had to figure them out, sure they could ask Jesus for help, but it’s still a remarkable story. Through Jesus, God’s children reached heights that David himself couldn’t have ever dreamed of.
So sure, study and follow Jesus. But everyone else in that story was remarkable and worth getting to know too.