JQuery tabs dynamic content with on click fadeout+fadein and slide without UI

Question

I am absolutely beginner in JQuery (but I've some knowledge about JS and programming on other languages)
I have 2 aims:

1. very simple tabs (or anything for controls), on click with old (active) tab content fading out and then clicked tab content fading in (same place)
2. same as 1 but with horizontal content slide instead of fading. I don't want JQuery UI, because that is overkill for a simple thing of this kind and I want to learn.

Aim 1, JS:

$(function () {
$("div.tabs > div:gt(0)").hide();
$("div.tabs ul a:first").addClass('selected');

$('div.tabs ul a').click(function () {
$("div.tabs > div").fadeOut('normal', function () {
$("div.tabs > div").fadeIn('slow');
});
$('div.tabs ul a').removeClass('selected');
$(this).addClass('selected');
   return false;
});
});

HTML:

<div class="tabs">
    <ul>
        <li><a href="#first">First</a></li>
        <li><a href="#second">Second</a></li>
        <li><a href="#third">Third</a></li>
    </ul>
    <div id="first">
        <h2>First content</h2>
    </div>
    <div id="second">
        <h2>Second content</h2>
    </div>
    <div id="third">
        <h2>Third content</h2>
    </div>
</div>

How to find active div, instead of poking all divs with $("div.tabs > div") in fadeOut and in fadeIn lines?

Aim2:
I read about slideUp and slideDown but that is vertical, perhaps I've to use animate()?
How? If it's too complicated than it is good for me with vertical slide...

Answer 1

Aim 1: Just add an active class to the current content div. See demo for altered code.

Aim 2: There are several techniques to do it w/o jQuery UI, depends on what you want to achieve and where you want to use it. See the altered demo for some sliding effects.

Answer 2

Paul's answer simplified for aim1: without additional classes, optimized to "div" + $(this).attr('href') and solution for fadeout is div:visible:

$(function () {
 $("div.tabs > div:gt(0)").hide();
 $("div.tabs ul a:first").addClass('selected');

 $('div.tabs ul a').click(function () {
  var newDiv = "div" + $(this).attr('href');
  $("div.tabs > div:visible").fadeOut('normal', function () {
   $(newDiv).fadeIn('slow');
  });
  $('div.tabs ul a').removeClass('selected');
  $(this).addClass('selected');
  return false;
 });
});

Thanks Paul.