What you want to do is relatively easy, if you are familiar with Wordpress Theme modifications. The following will assume you are at least comfortable with PHP, and hopefully Wordpress Theme modification. If not, I can provide some additional links in subsequent updates to this answer ... just let me know.
First step: Gravity Forms documentation has instructions for "Populating a Form Based On Another Submission". Specifically, see their section on "Setting up the first form to send data using confirmations". Use those instructions to pass your form field(s) to the desired the desired page(s) within your site.
Next: You will need to modify your theme's page template(s) (or create a child theme) to use those parameters for calculating which custom nav menu, dynamic sidebar, or other object to display. Use
$_GET to extract your parameters similar to the following:
dynamic_sidebar( 'custom-sidebar-a' );
dynamic_sidebar( 'custom-sidebar-b' );
dynamic_sidebar( 'custom-sidebar-c' );
dynamic_sidebar( 'custom-sidebar-WHATEVER' );
} // end switch
} // end if
If you are comfortable with PHP, but not so comfortable with Wordpress Theme modifications, you could use an intermediary plugin like Insert PHP Code Snippet to add a modified version of the PHP I provided to any widget area.
If you want to get really tricky, you could use the
$_GET value to set a cookie value, then use AJAX calls to change the sidebar/menu content in real-time. That is far more complex to setup. Please submit another Question, if you wanted to go that route.