SS External HD for my iMac catalina thunderbolt?

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You need a USB external SSD that includes a USB-A adapter/cable. An excellent choice is a G-Technology G-DRIVE mobile SSD R-Series Storage - Apple.

What are you trying to do with this external SSD?

Jack

If this drive will simply be used to store data instead of running macOS or other high-performance tasks, an SSD is not necessary. A high-quality 7200 RPM drive will give you much more capacity and be more suited for these tasks. A good choice is a SanDisk Professional G-DRIVE - Western Digital.

Jack

You can get a single large capacity HDD and partition it for TM and data, but understand if it fails, you lose all your stored data and your TM backup. At today's very reasonable prices, maybe better to have two 2GB drives rather than a single very large drive.

Pretty much any name brand spinner HD will work for you as data storage and TimeMachine. Just be certain you dedicate a drive to TimeMachine and get one about twice the size of your internal drive's capacity.