It's not best practice to use a drive that you have data on for backup purposes. You have a couple of choices:
1) You could partition either the HDD on your new machine (split the drive into two, one named partition for your backups, and one for your own data)
2) Partition the external drive in the same way.
Another, far better solution (and since the PC is new) would be to use Acronis True Image. It's not free, but it's the best backup software money can buy.
It will split your Internal or external drive for you, so that you don't have to do so yourself, and provided you make incremental backups weekly, it will restore your system to EXACTLY the way it was at the time of the last backup you made...Acronis can be found at:
You can get cheaper deals if you shop around....Amazon for example.