You can add anything you want to your
index.php to make it "stay there" forever. Or you can put the information in a post and use one of the WordPress Plugins like Adhesive or sticky to forced the post to stay at the top of the front page.
If you want random images to generate, there are a variety of ways to do it, and it doesn't have to be "in" a post but anywhere on any template file. I have a very simple one that rotates images in my sidebar when ever anyone reloads the page or visits a new page on my site. It's a PHP script and not a plugin called
rotator.php and I got it from http://www.hiveware.com/imagerotator.php and http://www.automaticlabs.com/ but you can use any of the many php scripts or WordPress plugins that do the same thing.
And do take time to explore the WordPress Codex, which is the main documentation site for WordPress as there are some really good articles in there that will help you learn how to work all this.