You can set WLM in Tools (Alt+M), Options, General tab to "Play sound when new messages arrive".
Afterwards, change your Sounds
settings to have a sound of your choice to play for the New Mail Notification
You can also install Windows Live Messenger and have it running with Windows Live Mail at the same time to get a pop-up in the notification area when you receive a new message. After you install it, click on the hotmail link in the upper right corner of Windows Live Mail to sign it and add that account for this to work.
Hope this helps,