Edit account creation message I'm trying to change the message users see after creating an account. It currently says:

Thank you for applying for an account. Your account is currently pending approval by the site administrator.
In the meantime, a welcome message with further instructions has been sent to your e-mail address.

What's the best way of changing this? Would the String Overrides module help? A Rule, perhaps?

Many thanks.
This is exactly what the String Overrides module is for.

If you only need just a couple strings, you can also use settings.php.  See this section:

/**
 * String overrides:
 *
 * To override specific strings on your site with or without enabling locale
 * module, add an entry to this list. This functionality allows you to change
 * a small number of your site's default English language interface strings.
 *
 * Remove the leading hash signs to enable.
 */


You don't want to use Rules, because although you can add a new message with a rule, the old message will still be there as well (which isn't what you want, I assume).