Re:
You need to be sure it's Mac OS compatible, although I'd use the iMac's Disk Utility to reformat it for Mac.
There are a few ways to back your iMac up – Time Machine is one of them but the option I used was to make a complete copy or clone of the iMac onto an external drive. You can use Disk Utility to create a 'disk image' or use apps like Carbon Copy Cloner. This means that absolutely everything is copied and the clone on the external is a fully bootable working startup disk. I've started up from my clone and immediately been able to work, surf the internet and access accounts with my same auto fill login details. I've even run the clone on my iMac at work. This is the beauty of a clone.