different sidebars for different page types

I am trying to have different sidebars for different page types on my underscores theme.
I want one sidebar for the index page (which is actually a static page), a different one for every “page”, and a third for all individual posts. So, three sidebars.

I’ve registered these sidebars in my functions.php, like so:

register_sidebar( array(
    'name' => __( 'Page-Sidebar', 'house-magic' ),
    'id' => 'sidebar-page',
    'before_widget' => '<aside id="%1$s" class="widget %2$s">',
    'after_widget' => '</aside>',
    'before_title' => '<h1 class="widget-title">',
    'after_title' => '</h1>',
  ) );

I also registered a sidebar-index. With this, they appear in my widgets panel.

I want to edit my sidebar.php code, so it will switch sidebars depending on page type (index, page, or post). I’ve tried this:

<?php if (is_page()) {
  $no_sidebar = !dynamic_sidebar('sidebar-page');
} else {
  $no_sidebar = !dynamic_sidebar('sidebar-1');
}

But it doesn’t work. I know I need another nested if statement to get it work for the index, but it’s not working at all as it is. When I test this sidebar code all the sidebars disappear.

I’ve also tried just editing page.php to call ‘sidebar-page’, but that doesn’t work either.

Any ideas of how I can do this?

Thanks a lot!

My site is house-magic.net