Eat external drive to easy more files to free up space

I recommend drives from OWC (MacSales.com) as they have proven reliability, excellent customer support and warranties.  Consider one of these depending on your budget and needs: 

OWC Mercury Elite Pro -HDD

1.0TB OWC Envoy Pro FX Thunderbolt 3 + USB-C Portable NVMe SSD

1.0TB OWC Envoy Pro SX Rugged Portable NVMe SSD with Thunderbolt/USB4

1.0TB OWC Envoy Pro Elektron USB-C portable NVMe SSD

Envoy Pro EX with USB-C or USB 3

OWC Envoy Pro SX - up to 2847 MB/s 

For your model contact OWC's customer support and get their recommendation for the SSD model that would best suit your iMac model and budget.  They may have additional models other than those I've shown above.

as already mentioned, just about any drive will work. but you shouldn't use any preloaded software (or install such software yourself) that supposedly makes the drive "Mac ready". when you use software from just about any manufacturer for their storage device you run the risk of that same software not being compatible with macOS updates / upgrades. it can cause the software to stop working. at best this will cause you a headache. at worst it can render your data inaccessible. it is always best to use disk utility to erase and format a drive before use to remove any preloaded software.

Just about any drive will work. I would recommend an SSD but a mechanical drive would work. I would format to APFS.