Is there a way to keep youtube videos from displaying on home page, and display only on single posts?

I would suggest utilizing the built-in excerpt functionality. An excerpt is basically a teaser for the rest of your post.

To utilize it: simply take the first couple paragraphs and copy them into the excerpt box on your post edit screen.

Depending on how your theme is built, you might not have to do anything to the code. However, if you try putting in an excerpt and the main content is still being displayed you will have to get your hands dirty and open up the template file that is calling the_content() on your blog listing page. Replace the_content() with the_excerpt() and you should be good to go!