Struggling with third person camera

Hi. I’m new to Unity

I wanted to try my hand at making my own third person camera without using Cinemachine. This is my script so far. It’s really basic, and while it does work for moving around the x axis, I don’t know where to go from here.

void Update ()
{
    float speed = 50; //camera movement speed
    float x = Input.GetAxis("Mouse X"); //get mouse axis movement
    float y = Input.GetAxis("Mouse Y");
    Vector3 cameraMovement = new Vector3(x, 0, y); //move the camera accordingly
    transform.Translate(cameraMovement * speed * Time.deltaTime); //////////////
    
    transform.LookAt(transform.parent); //camera is always pointed towards player    
}