BuddyPress.org

Yes you can use BP. As for your hosting, noted that some newbies have encountered problems setting up BP there but since you have WP experience, you would know what to do. You aren’t planning to go multisite there, are you? Re putting BP on a subdirectory – if you can, install WP/BP at root of new physical subdomain as in http://buddypresshere.yoursite.com/, to avoid any possible interference or conflict.