Things I need to accomplish:

1. Establish a "site variable" where we can set what category a blog belongs in. These categories are Option 1, Option 2, Option 3, and Option 4.
2. When one of the categories is selected, it generates the breadcrumb on the blog’s home page and also the first half of the secondary breadcrumbs in archive or single pages.
3. Make it so the blog home is automatically the second part of the breadcrumb link path.

Here are the screenshots that show the custom option called Site Information:

Writes to the wp_options database table

Here is the code so far:

class MySettingsPage
{
private $options;

function __construct()
{
    add_action( 'admin_menu', array( $this, 'add_plugin_page' ) );
    add_action( 'admin_init', array( $this, 'page_init' ) );
}

function add_plugin_page()
{
    // This page will be under "Settings"
    add_options_page(
        'Settings Admin', 
        'Site Information', 
        'manage_options', 
        'my-setting-admin', 
        array( $this, 'create_admin_page' )
    );
}

function create_admin_page()
{
    // Set class property
    $this->options = get_option( 'site_information_options' );
    ?>
    <div class="wrap">
        <h1>Site Information</h1>
        <form method="post" action="options.php">
        <?php
            // This prints out all hidden setting fields
            settings_fields( 'site-information_group' );
            do_settings_sections( 'my-setting-admin' );
            submit_button();
        ?>
        </form>
    </div>
     <?php
}

function page_init()
{        
    register_setting(
        'site-information_group', 
        'site_information_options', 
        array( $this, 'sanitize' ) 
    );

    add_settings_section(
        'setting_section_id', 
        'Custom Settings', 
        array( $this, 'print_section_info' ), 
        'my-setting-admin' 
    );  

    add_settings_field(
        'parent_category', 
        'Parent Category', 
        array( $this, 'parent_category_callback' ), 
        'my-setting-admin', 
        'setting_section_id'
    );      

    add_settings_field(
        'subcategory', 
        'Subcategory', 
        array( $this, 'subcategory_callback' ), 
        'my-setting-admin', 
        'setting_section_id'
    ); 
        
    add_settings_field(
        'blog_owner_email', 
        'Blog Owner Email', 
        array( $this, 'blog_owner_email_callback' ), 
        'my-setting-admin', 
        'setting_section_id'
    ); 
}

function sanitize( $input )
{
    $new_input = array();
    if( isset( $input['parent_category'] ) )
        $new_input['parent_category'] = sanitize_text_field( $input['parent_category'] );

    if( isset( $input['subcategory'] ) )
        $new_input['subcategory'] = sanitize_text_field( $input['subcategory'] );

    if( isset( $input['blog_owner_email'] ) )
        $new_input['blog_owner_email'] = sanitize_text_field( $input['blog_owner_email'] );

    return $new_input;
}

function print_section_info()
{
    print 'Enter your settings below:';
}

function parent_category_callback()
{
    printf(
        '<select id="parent_category" name="site_information_options[parent_category]" value="%s" >
            <option>Select...</option>  
            <option>Option 1</option>
            <option>Option 2</option>
            <option>Option 3</option>
            <option>Option 4</option>
        </select>',
        isset( $this->options['parent_category'] ) ? esc_attr( $this->options['parent_category']) : ''
    );
}

function subcategory_callback()
{
    printf(
        '<select id="subcategory" name="site_information_options[subcategory]" value="%s" >
            <option>Select...</option>
            <option>Option 1</option>
            <option>Option 2</option>
        </select>',
        isset( $this->options['subcategory'] ) ? esc_attr( $this->options['subcategory']) : ''
    );
}

function blog_owner_email_callback()
{
    printf(
        '<input type="text" id="blog_owner_email" name="site_information_options[blog_owner_email]" value="%s" />',
         isset( $this->options['blog_owner_email'] ) ? esc_attr( $this->options['blog_owner_email']) : ''
    );
}
}
if( is_admin())
    $my_settings_page = new MySettingsPage(); 

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