External hard drive to back up data from 2007 iMac 7,1

Pretty much any HDD will do. I stick with the major names like Western Digital, Seagate, Toshiba. You can format any of them to OS X Extended Journaled. Any HDD so formatted will work with both your current and new computer. Use Applications > Utilities > Disk Utility. USB 3.0 that is backward compatible to USB 2.0 is important. You should have USB 2 if your computer is newer than 2000. Size is your cost control factor. You don't seem to generate a lot of data so maybe a 1TB is enough. But the cost per GB is cheaper on 2TB and up devices. I buy mine on Amazon and go with the portables as I see no advantage to a desktop HDD and you never know when you'll want to carry it with you.

I should have added. If you search Amazon for Mac HDD you can find one preformatted with OS X Extended Journaled. These cost a little more and I save the money and format myself.

I'm glad I could help. And your thank you kinda made my day! So thank you too. And don't hesitate to come back. There's a lot of people who contribute here who want to help those with the need.

I am planning to buy the new 21.5" retina display iMac. Will I need to buy 1 external hard drive for my iMac 7.1 and a different one for the 2015 model?

If you plan on keeping BOTH iMacs, then you should consider getting a backup drive for each iMac. If you are going to sell/gift/recycle the older iMac, then get a backup drive large enough for the new iMac.

I agree that 1TB (terabyte) should be good enough for your current storage usage, assuming you do not get the camera bug or worse movie bug and start to store lots of image/movies on your iMac 🙂 The rule of thumb is that for Apple's Time Machine backup you should have about 3 times as much backup storage as your peek storage usage on your Mac. That gives Time Machine enough room to keep a good history of previous changed files, so you can go back in time to recover files that may have been deleted months ago, but you just noticed it was missing.

And yes, any USB3 external disk should work. If Time Machine does not automatically convert it to the correct format for you, then Applications -> Utilities -> Disk Utility -> Partition -> Options -> GUID partition table (1 partition is fine, it is the partition table type that is important). And then format the file system as "Mac OS Extended (Journaled)" and you are all set. But I think Time Machine will offer to do that for you as soon as you plug in the new disk it has never seen before (at least on the new iMac - not sure about a 10.5 Leopard iMac).