You can simply use your index.php as index page. Add a default loop and style the output to your needs.
Then – in your single.php file – just add links to the next/previous post using the template tag: get_next_posts_link() and get_previous_posts_link().
That’s the default way in WordPress to link to other posts/pages.
To make a link back to your index site, just use the home_url("https://wordpress.stackexchange.com/"); function.