What hard drive for backup do you recommend for 2013 iMac

As the iMac is a desktop computer, for Time Machine I use desktop-class 3.5-inch external drive enclosures with their own independent power supplies. Cheaper "bus-powered" externals too often fail to get enough power from the computer to work properly.

I use these: https://eshop.macsales.com/shop/owc-mercury-elite-pro. My iMac 5K 2017 has two attached; one doing Time Machine backups and the other doing bootable Carbon Copy Cloner backups.

I install a quality SATA 6G 3.5-inch hard drive in the enclosures—takes only minutes. Currently I am using WD "Black" series drives.

SSD's are faster but not as reliable yet as a quality mech drive. You do not need the speed of an SSD for Time Machine backups once the first backup is complete.

If you use the external for a scratch disk for something like Photoshop, the SSD external speed may be beneficial.

The main advice would be to get at least two hard drives, and make two backups – maybe staggering the dates at which you update them.

Backup drives can fail, and the worst time to discover that your only backup drive has, is when you need it …