Is Wi-Fi always favoured over other data connections? I am at home and I would like to be sure that the data connection is always going through the Wi-Fi rather than the (expensive) data connection. 

Is it enough to simply turn on Wi-Fi and connect to the (password protected) network? How can I control that the download is happening through the right connection? Can sleep (or other events) disable/change/toggle this setting?
In Android, AFAIK, when you connect to an active Wi-Fi network, mobile data (GPRS, 3G, etc) will be disabled (even if are turned on) temporary. So it would be OK to just connect to the Wi-Fi network. But, if you want to be sure about disabling mobile data, you should go to Settings -> Wi-Fi and Networks -> Mobile Data and uncheck the option to disable mobile data.
(in ICS it's in Settings -> Wireless and Networks -> More -> Mobile Networks)