However would it be better to back up my laptop to an external hard drive connected to my desktop?
I wanted to create system images of both my laptop and computer as well and store these on the external hard drive. Backblaze can apparently backup external drives as well. This way my laptop files would not interfere with the ones on my desktop. Not that I am sure it would, but just in case.
What do you guys think?
It won't make much difference. It might be wise backing up to the external drive if the backup is big and you have limited space on the main drive.