Need more info in regards to what you actually want, but GoFlex looks like a USB drive, so unless your router can support USB drives, it's not going to be wireless and will need to be plugged into a computer for copying stuff to it.
Backup up ultimately comes down to how paranoid you want to be, effort you want to put in it and how much do you want to pay? The rest is getting a routine down that works for you and sticking to it.
For one, lets say you had the GoFlex and was copying (or backing up) the data on your computer to it. It's not really a backup until you have 1 or more copies of said backup/drive of the files you care about (my opinion).
The best backup solution in my opinion is to have at least one onsite and at least one offsite backup. The reasoning behind this is if your onsite solution fails for some reason you have a backup for the backup. And more importantly, if a fire happens or your local device dies, you can hopefully rely on the offsite one.
Last edited by cgwahl; 10-15-2011 at 13:05..