This plugin does the same thing as what you are looking for: http://wordpress.org/extend/plugins/magic-action-box
It has a custom post type called action-box but has different types of action boxes that you can select when you create a new action box. The code you want is found inside the plugin’s directory lib/classes/ProsulumMabAdmin.php.
Look for the method add_actions() and at the very end you should find something like this:
/**
* Hacky part followed from Premise. This is to make sure people
* select an Action Box type before an Action Box type is actually created.
* Requirements as of WP3.3: Custom post type needs to have support for comments
* for this hack to work
*/
add_action('admin_notices', array( &$this, 'possiblyStartOutputBuffering' ) );
add_filter('wp_comment_reply', array( &$this, 'possiblyEndOutputBUffering' ) );
Follow the code – or just copy it and mod as needed, that’s what open source all about 🙂 – and you should be able to create your popup option page to select the type of event.
But, you also need to catch the selection of event type. For how Magic Action Box does it, again look at the method add_actions() and look for
add_action( 'admin_init', array(&$this, 'processSubmissions' ) );
follow the code and you’ll find a section within the processSubmissions() method that processes the selection of an action box type.