In your theme's header.php, there's code
<li<?php if (is_home()) echo " class=\"selected\""; ?>>
<a href="<?php bloginfo('url'); ?>">Home</a></li>
Delete that to get rid of the "double" home in the navigation bar. [You can edit the file locally and re-upload, edit on the server if you have shell access, or edit through WordPress's Presentation > Theme Editor interface.]
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So, the above is an answer to your question
How do I make the home page static and not have the other "home" button show up?
Do you still need help with the earlier question -
Is there a simple way to set up a page that is the "front page" for the blog?
[I answered that and don't know a simpler way to do it. If my answer wasn't clear, let me know...]