In the web panel, click on "Web" under "Domains" on the navigation bar to the left.
Then on the line for your domain on the right, you want to click on the "Edit" link.
A new page on the right will appear. Under "A Fully Hosted Domain", there is a line that starts out "Web Directory:"
This line specifies the directory where your index.html home page should go. If you don't like "public_html" or "www.mydomain.com", you can rename this directory if you want.
And yes, if the directory doesn't exist, you need to create it.