Which filter/hook to use for styling comments?

the comments_form function that outputs the contact form has two actions that could be used to accomplish what you want.

add_action( 'comment_form_before', 'wwm_comment_form_before' );

function wwm_comment_form_before() {
//output your opening html here
}

add_action( 'comment_form_after', 'wwm_comment_form_after' );

function wwm_comment_form_after() {
//output your closing html here
}

and that’s a wrap 🙂