Rigidbody grid based movement in a 3D game

Hey, i am new to unity ( Probably not the first time you have heard that...) and i have a small movement script that moves a 1 by 1 cube in a grid like plain on the X and Z axis in a 3D environment.

 using System.Collections;
     using System.Collections.Generic;
     using UnityEngine;
     
     
     public class Movement : MonoBehaviour
     {
         private bool canMove = true, moving = false;
         private int speed = 15;
         private Vector3 
 
 
 void Update()
         {
             if (canMove) 
                         
             {
                 pos = transform.position;
                 move();
             }
             if (moving)
             {
                 if(transform.position == pos)
                 {
                     moving = false;
                     canMove = true;
                     move();
                 }
                 transform.position = Vector3.MoveTowards(transform.position, pos, Time.deltaTime * speed);
             }
             
         }
         private void move()
         {
             if (Input.GetKeyDown(KeyCode.UpArrow))
             {
                 canMove = false;
                 moving = true;
                 pos += Vector3.forward;
             }
            //This is repeated for every arrow key to move in all directions.
         }
     }

The movement is working just the way i want it to, when i press the arrow keys the cube moves to the according direction one length of the cube ( does that make sense?).

So my problem comes in when i try to add physics to the cube (trying to make invisible walls to limit the players movement).

When the Cube collides with an object it goes crazy ( glitching all over the place) i am pretty sure that is caused by the transform.position lines, i think those don't take the rigidbody physics into mind when moving my object?

So i probably need to change those, but i don't know to what command, i have searched google but these type of questions are hard to google since i don't really know what to look for.

So can any of you help me convert the code so that:

1. The cube moves smoothly to the next "grid"

2. The cube is affected by gravity and cannot pass trough certain objects/walls

3. It's simple so i actually know what is happening since this project is just a learning type situation.

Thanks in advance if you can help me :)