F-Zero Game - Collisions/Physics.

Hello World, :D I have been working on a sci fi racing game similar to F-Zero and I have been wondering about something. I have a script that gives the basic steering controls (Accelerate Forward, rotate left and right) but I have been struggling with the physics and collisions. Whenever I turn the speed right up on my player, it flies straight through any oncoming objects, how can I fix this?. Secondly, I need to make my player stay "upright" at all times (so that you don't flip over when turning etc.) and whenever i put a rigidbody onto the player, the ship stutters whenever the player accelerates (ends up flipping over). Finally, how could I make my ship hover a tiny bit?

So, if anyone is willing to help me fix this problem I would be EXTREMELY thankful as this is my major work for my last year of school :)

Here's my control script:

//really basic, stupid code i came up with

     var speed : float = 10.0;
     var rotationSpeed : float = 100.0;
     function Update () {
         var translation : float = Input.GetAxis ("Vertical") * speed;
         var rotation : float = Input.GetAxis ("Horizontal") * rotationSpeed;
         
         translation *= Time.deltaTime;
         rotation *= Time.deltaTime;
         
         transform.Translate (0, 0, translation);
     
         transform.Rotate (0, rotation, 0);
     }

What I'm aiming for:

https://www.youtube.com/watch?v=RZ1KWVeHP0o

(without the antigrav setup)