BuddyPress.org

The only issues you should have with a WP theme is all the BuddyPress CSS, easy enough to fix but can require lots of edits depending on the theme.
To include the required BuddyPress JS & ajax functions in any WP theme, all you need to do is add something like the following to your themes functions.php file

require_once( BP_PLUGIN_DIR . '/bp-themes/bp-default/_inc/ajax.php' );
function theme_loaded_init() {
wp_enqueue_script( 'bp-js', BP_PLUGIN_URL . '/bp-themes/bp-default/_inc/global.js', array( 'jquery' ) );
}

add_action('wp_head', 'theme_loaded_init', 5);


You would also need to add the BuddyPress template folders to your theme & add either the default buddypress & admin bar css to your css with edits or include the defaults in the above theme_loaded_init function.

also note, some themes that include custom JS can conflict with BuddyPress JS, if the theme is coded properly it should be easy to remove those conflicts on BuddyPress pages.