WordPress plugin: Getting posts where checkbox selected

Just use Post tags.

Every post in WordPress can be filed under one or more Tags. This aids in navigation and allows posts and to be grouped with others of similar content. (from Codex)

You can query posts in various ways. Most solid is of course the wp_query class. Use it like this:

// The Query
$args = array('tag' => YOUR_DESIRED_TAG_SLUG);
$the_query = new WP_Query( $args );

// The Loop
if ( $the_query->have_posts() ) {
    echo '<ul>';
while ( $the_query->have_posts() ) {
    $the_query->the_post();
    echo '<li>' . get_the_title() . '</li>';
}
    echo '</ul>';
} else {
// no posts found
}
/* Restore original Post Data */
wp_reset_postdata();

More on querying by tag: http://codex.wordpress.org/Class_Reference/WP_Query#Tag_Parameters

Also, if you don’t want to waste post tags for that, you can create custom non-hierarchic taxonomy, which is, again, built-in WordPress sollution.