I think what you are looking for is triggered mailings (requires login).
To send a single mail to the new Contact, you can specify a notification Page URI in the
contact.Save call like this:
string notificationPageUri = ConfigurationManager.AppSettings["Subscribe.NotificationPageUri"];
contact.Save(notificationPageUri ?? String.Empty);
But a triggered mailing is specifically for generic situations like Contact registration or performing an action (like clicking a link).
There are no events that run on creation of Contacts, so there is nothing you can hook into that way. I once tried a hack by using a TBB in the confirmation email Page Template, but if I remember correctly, that is rendered only when it is tested and the rendered result is used for the mail, so it didn't even work.