Do I only need to import style.css for a child theme?

This question depends entirely on the Theme in question, and how it handles CSS.

1. For a Theme that uses only a single style.css file, obviously, you only need to import style.css.
2. For a Theme that links other stylesheets in the document head (they shouldn’t be doing this; instead, they should be properly enqueueing them), you’ll need to determine whether or not you want to leave those links in header.php, based on whether or not you want to use the styles defined in those stylesheets.
3. For a Theme that enqueues additional stylesheets, via wp_enqueue_style(), you don’t need to do anything. Such stylesheets will continue to be enqueued in the Child Theme. If you don’t want those styles, then you need to dequeue those stylesheets, via wp_dequeue_style() in the Child Theme functions.php.
4. For a Theme that prints styles in the document head, via add_action( 'wp_print_styles', $callback ), you don’t need to do anything. Such stylesheets will continue to be printed in the Child Theme. If you don’t want those styles, then you need to override the output of those stylesheets, via remove_action( 'wp_print_styles', $callback ) in the Child Theme functions.php.

I think that covers most of the bases.