How to redirect /user to /user/UID, for logged in users?
If you were handcoding this, you would create a menu path using hook_menu, with %uid as the second parameter. And the page_callback value of the menu item would be the function rendering the user page. You will then use hook_user_login to set the redirect rule.

If you were doing this using contrib modules, I suggest you looking into profile2, it comes with a built in functionality where each user has their own profile page.

edited:
The last sentence on your question, makes me led to think that the user/%uid path needs to be accessible users/visitors other than the owner. So let's here is how you would do it.


Create your custom module, let's call it ea_custom for the sake of
this example. 
Add hook_menu and page_callback to your ea_custom.module and register the path for the individual user page.

/* Implements hook_menu */
function ea_custom_menu() {
  $items['users/%user'] = array( //the %user will be used as argument for the page callback
    'title' => t('User Profile'),
    'page callback' => 'ea_custom_render_userpage',
    'page arguments' => array(1), //zero base array. This tells hook menu to first load user with the specified uid specified by %user parameter.
    'access callback' => 'user_access', //so non-onwer can also view it
    'access arguments' => array('access content'),
  );
  return $items;
}

/**** page callback for users/%user ****/
function ea_custom_render_userpage($user) {
   //you now have accessed to the user object
   drupal_set_message('' . print_r($user, TRUE) . '');

//assemble your output using the values inside $user object
   $output = $user->uid; //etc.. etc...

return $output;
}


Additional notes: you can use different methods to get values from entity objects such as user and node. I would recommend you to check entity_metadata_wrapper for one. Also, instead of using %user, to get user object, you could opt to use %profile2, since you have that module installed, and it will allows you access to fields you have attached to profile type.

wow, I can't seem to format this properly. Here is the paste bin: http://pastebin.com/kiv6GfPN