What I wish to know is, how do i implement my already made index.php file to use custom posts it. (See below)

What I wish to accomplish:

Display all posts(already accomplished in index.php)
--> show normal post a.k.a 'Article' (already accomplished in index.php)

If category/or post type 'Aside' is used, don't apply a <a> tag, make title lighter(can figure it out in CSS)
-->show text for the 'Aside' marked post

If category/or post type 'Link' is used,  wrap title in <a> tag linking to a site(<-- how would I do that in WordPress?)  
-->show text for info about the link

If category/or post type 'Photo' is used, don't wrap title in a <a> tag
-->show attached image in post, and post text as a caption

I understand this might seem like a great deal but I am sure it's easily do-able.

Some source code might not assist me to completely, and so i have my index.php below to try to assist me to implement it in it:

<?php get_header(); ?>


<?php if (have_posts()) : ?>

    <?php while (have_posts()) : the_post(); ?>

        <div class="post" id="post-<?php the_ID(); ?>">

            <article>
            <!-- <p><span class="metaCat"><?php the_category(', '); ?></span></p> -->
            <h1><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a></h1>
            <p><span class="meta"><?php the_time('F jS, Y') ?></span></p>
            <hr />
            <div class="entry">
                <?php the_content('Read the rest of this entry &raquo;'); ?>
            </div>

        </div>
</article>
        <hr class="big" />
    <?php endwhile; ?>



<?php else : ?>

    <h2 class="center">Not Found</h2>
    <p class="center">Sorry, but you are looking for something that isn't here.</p>
    <?php include (TEMPLATEPATH . "/searchform.php"); ?>

<?php endif; ?>

If you're able to input the appropriate code right into a workable index.php file you're going to get some well considered brownie points!

Thanks and all sorts of assistance is welcomed!

I finally see that which you designed to do here. This really is easily done while using get_publish_format() function. Just replace the title here with:

<?php
$format = get_post_format(get_the_ID());
if ($format == 'link') { ?>
<h1><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php  the_title(); ?>"><?php the_title(); ?></a></h1>
<?php }else{ ?>
    <h1><?php the_title(); ?></h1>
<?php } ?>

Another bit about connecting to some site though, I am unsure how you need to accomplish this. Are you currently mentioning towards the blogroll?

The best choice for that "link" publish format, is by using a custom metabox/custom fields.. add your key as "URL" then type the address within the value area.

Use get_publish_meta() to obtain the URL and employ that rather than the_permalink() within the href.