random post from wordpress into new html/php page

I would like to create a new page outside of wordpress. My wordpress is in a folder. So for the index page, that is not in the folder, I would like to set that up so that when I want to show a post from the wordpress blog in the nonwordpress index page. How do I do that?
For example, the index.php in the folder isn’t the one I want to show to the public. It is only for my friends and myself.
But the index.php on the main page, that is the page I want to design and put a few posts only to show the public. And those posts would not leave the index.php, nor would new posts appear on the index.php unless I put in the specific code for the post in the index.php.