Take a look at the WordPress documentation for that function. Basically, without parameters, it will log the user out in place. If you logout in a users-only area, it’ll take you to the login page for that area.
Here is Wordpress’ suggested link for redirecting to the homepage: <a href="<?php echo wp_logout_url( home_url() ); ?>">Logout</a>
So in your case, you’d want to adjust that, of course, to something like
Thanks I actually worked it out on reading the codex - sorry for wasting your time as I tried to respond here but the admin blocked me out for a spam reason or something. Great answer though so hopefully someone else benefits.