How do I add CSS options to my plugin without using inline styles?

Use wp_register_style and wp_enqueue_style to add the stylesheet. DO NOT simply add a stylesheet link to wp_head. Queuing styles allows other plugins or themes to modify the stylesheet if necessary.

Your stylesheet can be a .php file:

wp_register_style('myStyleSheet', 'my-stylesheet.php');
wp_enqueue_style( 'myStyleSheet');

my-stylesheet.php would look like this:

<?php
// We'll be outputting CSS
header('Content-type: text/css');

include('my-plugin-data.php');    
?>

body {
  background: <?php echo $my_background_variable; ?>;
  font-size: <?php echo $my_font_size; ?>;
}