How to use jquery and wp_enqueue_script

I´ve spent a good while trying to figure this out. Im trying to add a script that need an external jquerylibrary. I can make it work by inserting my script between scripttags, however i understand thats not the correct way to do it, and it breaks another script on the site.

I spent a fair amount of time tonight trying to figure out how to add the script correct, and i just cant get it.

I understand something like this is the correct way to enqueue the script:

function my_scripts_method() {
wp_register_script( 'jquery', 'http://code.jquery.com/jquery-1.9.1.js');
wp_enqueue_script( 'jquery' );
}
add_action('wp_enqueue_scripts', 'my_scripts_method');


My main question is, how do i write my functions so it calls the library, and at the same time failsafe it so it only loads once, and doesnt crash with other scripts? This is the script:

$(document).ready(function () {


$("#menu-item-16").hover(




          function () {
                  $('body').css("background", "#ff9900");
              }, 
              function () {
                $('body').css("background", "#ccc");
             }
            );

            $("#menu-item-17”).hover(
              function () {
                  $('body').css("background", "red");
              }, 
              function () {
                  $('body').css("background", "#ccc");
              }
            );

            $("#menu-item-18”).hover(
              function () {
                  $('body').css("background", "yellow");
              }, 
              function () {
                  $('body').css("background", "#ccc");
              }
            );
        });

Edit:

Second question, several librarys and a stylesheet.

As said above i have a little more complex script that you guys might be able to help me out.

I have this code in the header right now, and it works.

   `<link rel="stylesheet" type="text/css" href="/wp-content/themes/neighborhood/js/jquery.fullPage.css" />

    <script src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>

<script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.9.1/jquery-ui.min.js">     </script> 
 <script type="text/javascript" src="/wp-content/themes/neighborhood/js/vendors/jquery.slimscroll.min.js"></script>

<script type="text/javascript" src="/wp-content/themes/neighborhood/js/jquery.fullPage.js"></script>



<script>
 $(document).ready(function() {
$.fn.fullpage({
    verticalCentered: true,
     resize : true,
    slidesColor : ['#AF1700', '#359973', '#F46321', '#A6C7DB'],
    scrollingSpeed: 700,
    easing: 'easeInQuart',
    menu: false,
    navigation: false,
    navigationPosition: 'right',
    navigationTooltips: ['firstSlide', 'secondSlide'],
    slidesNavigation: true,
    slidesNavPosition: 'bottom',
    loopBottom: false,
    loopTop: false,
    loopHorizontal: true,
    autoScrolling: true,
    scrollOverflow: true,
    css3: false,
    paddingTop: '3em',
    paddingBottom: '10px',
    fixedElements: '#element1, .element2',
    normalScrollElements: '#element1, .element2',
    keyboardScrolling: true,
    touchSensitivity: 15,
    continuousVertical: false,
    animateAnchor: false, 
    setScrollingSpeed: 1000,



});
});    

 </script>

`

From my newfound insights, i tried this, and it didnt work:

`

function fullpage() {     wp_enqueue_script('jquery');  

    

wp_register_style( ’fullpage-css', get_template_directory_uri() . '/js/jquery.fullPage.css','','', 'screen' );   
wp_register_script( 'jquery.1.8.3', get_template_directory_uri() . 'http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js', array('jquery'),'',true  ); 
 wp_register_script( 'jquery.1.9.1', get_template_directory_uri() . 'http://ajax.googleapis.com/ajax/libs/jqueryui/1.9.1/jquery-ui.min.js', array('jquery'),'',true  ); 

 

 wp_register_script( 'fullpage', get_template_directory_uri() . '/js/jquery.fullPage.js', array('jquery'),'',true  ); 
 wp_register_script( 'fullpagecode', get_template_directory_uri() . '/js/fullpagecode.js', array('jquery'),'',true  ); 
 wp_register_script( 'slimscroll', get_template_directory_uri() . '/js/vendors/jquery.slimscroll.min.js', '', null,''  ); 

wp_enqueue_style( 'fullpage-css' ); // Enqueue our stylesheet

    

wp_enqueue_script( 'jquery.1.8.3' );  // Enqueue our first script

 

 wp_enqueue_script( 'jquery.1.9.1' ); // Enqueue our second script

 

 wp_enqueue_script( 'fullpage' );  // Enqueue our third  script

    

wp_enqueue_script( 'fullpagecode' ); // Enqueue fourth script

 

 wp_enqueue_script( ’slimscroll’ ); // Enqueue fifth script

  

  }add_action( 'wp_enqueue_scripts', ’fullpage’ ); `