As usual, Cory is correct, in regards to trying to upgrade the internal drive on the iMac. I will say, though, that when I was using my late 2012 Mac Mini with its slow, Hitachi 1 TB 5400 rpm drive, it definitely was not a speed demon. And as most folks know, I take care of my machines very, very well. I keep them "lean, mean, and clean", I always insure to having the latest version of any software I have, avoiding any "nefarious" third party software, not using any virus software, etc., etc. And besides daily disk cleanup, I always go through my disk cleaning/maintenance/repairs, and backup, processing once a week, typically on Saturdays. The tools I use for that are Onyx, TechTool Pro, and SuperDuper!. And when I had that drive inside the machine, I would also use TechTool Pro's Volume and File Optimization features to keep things "straight" on the drive. But even with all that, the machine was still no speed demon.
The upgrade to the SSD, though, sure changed that! The machine became a real pleasure to use, and that 1 TB drive was still put to good use as a storage device.
Now, an external SSD is a very good option. Thunderbolt connectivity would be the fastest, but be aware that external enclosures with such connectivity are expensive. Since you have USB 3.0 ports on your iMac, you might want to consider using an external enclosure with USB 3.0 ports/interface. I have 2 external Orico enclosures with USB 3.0 ports, and inside each of them I have a (fast) Samsung 850 Pro 512 gig SSD. When I boot either of my Macs from either enclosure (I have SuperDuper! bootable backups for each machine on both devices), boot time of course is "somewhat" slower than booting each machine directly (from the respective internal SSD), but with those external SSDs, it's much faster than with a conventional HDD. Once on that external enclosure, apps do run fast.