I would set it up like this:
The Google Apps Mail
Instal unity-mail & unity-webapps-gmail
sudo apt-get install unity-mail unity-webapps-gmail
Open Unity mail and configure it for Google Apps. Setting it up is almost the same as for a gmail account, except for the username which is email@example.com
You can even set it up with URL so that when you click a mail under the message notification tray you will go directly to the inbox...
The Outlook.com mail
Unfortunately Outlook.com does not support IMAP yet, so I would set up forwarding to a gmail account I would create only for this purpose and then set up a second account in unity mail..
Alternatively you can use extentions for your browser:
If you are using chrome go for Outlok.com notifier
And if you use Firefox: X-Notifier