Use multiple email addresses on contact form
Despite being an old post, I think it warrants an answer for those sites still operating on Drupal 7 or even Drupal 8.  Rather than use the built-in Contact form, I recommend using the Webform module.  Below is a description of how it can be used for a contact form of this nature, with Drupal 7 specific screenshots.

If you setup your contact form using the Webform module, you can setup distinct emails, one for each purpose.  In both cases, the "from" setting can be set to one unique site email address, a preset/predefined email address in the configuration, or one email address from the form itself.