Time machine

It make incremental copies and should be larger than the source (your iMac). You can select folders not to back up if you don't need to backup everything.

Another option is a Synology NAS (they all support Time Machine)

 

Only if your 1TB is full. Initially they will both be full the same way but as Time Machine starts saving multiple versions of files that one will get more and more full. However, it deletes older files automatically so you don't need to worry.

I'd get one slightly larger than your internal to be on the safe side. I have a 640GB internal and 1TB external (for Time Machine) on my iMac. The internal has 200GB free, the external is full but it has versions for the past 3 years

 

Time Machine backs up your entire drive (excluding the things you choose to exclude) on the first time you run it.
After that, it then copies over only those files that have changed.

If you have a 500MB file, and you change its name, it will be copied again. If you change its name again, you will have 3 copies of that file.

Most files on your computer do not change. A lot of the System files and Applications, for instance. Your iTunes files are unlikely to be modified.

Ideally, you want more space than is USED on your hard drive.

TM will delete old backups if the backup drive is full.