Small external backup device suggestion for iMac?

You need an external HD for doing Time Machine backups, you should be backing up the old computer with TM at least daily and when the new Mac is up and running use the same Time Machine External Hard Disk to backup the new computer. So here is what I recommend:

• .Contact www.macsales.com and purchase an OWC Mercury Elite Pro, a 2TB or 4TB is fine.
• Once the new External Hard Disk. arrives please follow the steps in Back up your Mac with Time Machine - Apple Support
• The once the new Mac arrives follow all the steps in Setup Assistant and Migration Assistant - Apple Community

And you are done. Step #2 can take up to 5-6 hours as it is the first backup, subsequent backups generally take less than a minute. Why, because the first backup is backing up everything, the subsequent backups only backup new or changed files.

Finally, please note that iCloud is NOT for backing up, it is designed to sync files between your various devices. For example, I am currently on vacation (yeah I know why am I writing this then….) While I’m out I use my iPhone to take photos. When I get back and want to edit the photos I just open my iPad and use that for editing. Then when I get home I open the photos app, my photos are there and I can look at them on my computer, share them, display them on my Apple TV etc. That is what iCloud is for!!! Time Machine is for backing up your iMac, you can also backup your iPhone and iPad using iCloud storage but NOT backup your Macs using iCloud!

Just to clarify,

The External drive, should not be considered a one time use. You should, as mentioned be backing up consistently.

So you can recover files in case of disaster.

With that said, any drive out there will work fine. There no specific type of drive for Macs to any specific one for Time Machine either.

Not sure what you are aiming at with a "small device"? Do you mean as in physical size, or in capacity? Also small as opposed to what, or in relation to what? Most drives will be much smaller than the Mac, but some may be larger than a mouse. Size is pretty relative.

Most external drives, have a pretty small footprint in general though.

For example, here's a 1TB HDD, which would work fine for Time Machine backups.

click here ➜ Seagate Portable 1TB External Hard Drive HDD - Amazon.com

You will need an adapter to connect it to the new M4 iMac though.

click here ➜ Ugreen USB-A to USB-C adapter - Amazon.com

If budget is a concern you should consider getting a Mac Mini M4 with 16 GB RAM and a 1 TB SSD. And pair that with a 27" or 32" 4K 3rd party monitor. This will be $600 less than a similarly configured 24" M4 iMac.

I just got a Mini configured as above with a 32" 4K monitor and it is excellent. The only concession is you need to turn on and off the monitor separately from the Mini when you use it.

As far as getting your files to the new Mac you should follow rkaufmann87's recommendation of getting a 2GB or larger external drive, backup your old iMac, and then when you first open your new Mac with the Time Machine drive plugged into the new Mac and are asked to migrate your files select the TM drive. It will bring over all 3rd party apps with their settings and activation codes along with your user files.

For what it's worth the savings you'll achieve with a Mac Mini can easily pay for an SSD Time Machine drive of sufficient size. I use this setup for my Mini:

I use the 4 TB model as I'm backing up 4 external SSD drives with TM.

What do you mean by a "onetime use"?

What are you considering replacing the 27" iMac with?

Is budget a concern?

I agree, your post is lacking in detail so we really have no idea what to recommend and why. Please try to be specific and don’t leave out details.