How to store page visit counts?

You can use custom fields for this. What I would suggest is setting up a shortcode you can put on any page you want to show the counter. For an extremely basic example with no HTML formatting, you can do this:

add_shortcode( 'examplecounter', 'counter_shortcode' );
function counter_shortcode( $atts, $content = null ) {
    global $post;
    if( isset( $post->ID ) ) {
        $current_count = get_post_meta( $post->ID, '_counter_custom_field', true );
        $new_count = $current_count === '' ? 1 : $current_count + 1;
        update_post_meta( $post->ID, '_counter_custom_field', $new_count );
        return $new_count;
    }
}

And now you can place [examplecounter] anywhere in a post and it should start counting for you. 🙂