Your iMac is approaching 6+ years. Is the internal drive the original one? That could be the next problem you face. Six years is a very old age for a mechanical drive!
OTOH, if that internal drive is less than 2 years old, you could probably get by simply with an external USB 3 drive. I suspect Apple will continue having USB 3 ports for some time, so, even if you get a new Mac, you can still use that drive with it.
When most of us here talk about external drives, we're really talking about "enclosures". The drive can be the external ones you already have, assuming they are fairly new and you ditch the second failed 3TB Seagate. Since I'm talking about external drives, the only decision is what kind of interface (USB 2, USB 3, Thunderbolt, or FireWire) to buy. You already have recommendations for the actual drive.
While you
do have FireWire, and it would be much faster than USB 2, those enclosures are:
1. More expensive
2. Apple no longer has FireWire ports in new iMacs.
Thus, unless that enclosure had another interface (USB 3?), you'd have to buy a new
enclosure when you get the new Mac. Fortunately, enclosures are the least expensive item we're talking about.
Looks like a
USB 3 enclosure is your current, least expensive option. Just be aware that it won't be any faster than your
current drives until you buy a new Mac. A USB
3 device running on a USB
2 machine will slow down to USB
2 speeds.
Thunderbolt would be even faster, but you don't have that port now,
so you'd have to buy a new Mac to use it!
I hope you've been saving your
pennies dollars!
Edited for, hopefully, better clarity and understanding