Hello,
I’d say the simplest way would just be to hide the menu on the homepage through your Custom CSS.
.home #access { display: none; }
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For CSS changes, it’s a good idea to use a tool like firebug or Google Chrome’s built-in developer tools to locate them and then put the edits either in your child theme or in the “Custom CSS” option on your theme options page.
Also, here’s a helpful tutorial on how to use Firebug – http://vimeo.com/20917974. The only thing I’d suggest not doing is actually making edits to the theme’s CSS files, as it shows at the end of that video. However, the video serves as a good introduction to Firebug and how it can be used to find what CSS is effecting certain areas of your site without ever digging around in any files.