Which escape function to use when escaping an email or plain text?

Yep, you can escape it as normal HTML, like so:
<?php echo esc_html( $email ); ?>

For the mailto link, you can use esc_url. Just make sure you include mailto: into the URL, e.g.:
<a href="<?php echo esc_url( 'mailto:' . $email ); ?>">

So a fully escaped mail link would look like this:
<a href="<?php echo esc_url( 'mailto:' . $email ); ?>"><?php echo esc_html( $email ); ?></a>