Rigidbody First Person Controller Movement

Hey guys! I am hoping that someone can guide me through this issue I have been having for the past 2 weeks or so. I am trying to make a plain old rigidbody first person controller in Unity 5.4.1. I can't seem to figure out how to make my player move correctly. I need the player to move almost instantly but with half a second or so of acceleration and deceleration. I would not like to use axis inputs but rather individual buttons. Keep in mind that I do NOT have a standard CharacterController component on my player. I will post a screenie of my editor window. Here is my code so far (minus the movement):

 using UnityEngine;
 using System.Collections;
 
 public class CharacterController : MonoBehaviour {
 
     public Rigidbody rb;
 
 
     // axis input vars
     public float walkSpeed = 5.0f;
     public float walkAcceleration = 0.1f;
 
     float forwardSpeed = 0.0f;
     float backSpeed = 0.0f;
     float rightSpeed = 0.0f;
     float leftSpeed = 0.0f;
 
 
     // sprint vars
     public float sprintSpeed = 10.0f;
 
 
     // mouse input vars
     public float mouseSensitivity = 5.0f;
     public float upDownRange = 80.0f;
 
     float verticalRotation = 0;
     
 
     // use this for initialization
     void Start () {
 
         Screen.lockCursor = true;
 
         rb = GetComponent<Rigidbody>();
     }
     
     void Update () {
 
         if (Input.GetKeyDown("escape"))
             Screen.lockCursor = false;
 
 
         // sprint
         if (Input.GetButtonDown("Sprint")) {
 
             forwardSpeed = sprintSpeed;
         }
 
         if (Input.GetButtonUp("Sprint")) {
 
             forwardSpeed = walkSpeed;
         }
     }
 
     void FixedUpdate () {
 
 
         // mouse inputs
         float rotLeftRight = Input.GetAxis("Mouse X") * mouseSensitivity;
         transform.Rotate(0, rotLeftRight, 0);
 
         verticalRotation -= Input.GetAxis("Mouse Y") * mouseSensitivity;
         verticalRotation = Mathf.Clamp(verticalRotation, -upDownRange, upDownRange);
         Camera.main.transform.localRotation = Quaternion.Euler(verticalRotation, 0, 0);
     }
 }

Any help is MUCH appreciated as I have tried just about everything google has to offer and would eventually like to release this as a game. Thank you!