Several thoughts here, Rob:
1) "Mobile" drives usually do not have an independent power supply and, in my experience, are less reliable than an external WITH its own power source.
2) As an iMac is seldom considered "mobile," a full-size drive with independent power is far more appropriate to any desktop computer.
3) An SSD is overkill for Time Machine. A fast, quality mech hard drive is plenty fast after the initial backup
4) Any speed benefit of an SSD is greatly reduced by the USB2 ports on your Mac.
5) You will need an adapter to use a drive with USB-C connectivity on the USB-A ports in the 2009 iMac. More cost.
We use three OWC Mercury Elite Pros, two on my 2017 iMac and one of Mrs AJ's 2011 USB2 iMac. The one I would recommend for your FireWire 800 equipped iMac is this one:
https://eshop.macsales.com/shop/firewire/1394/USB/EliteAL/eSATA_FW800_FW400_USB
It has an independent power supply and come swith cables.
FW800 will be faster than USB 2 on your iMac. You can get one with a drive already installed.
I buy the bare/empty enclosures and install WD "Black" series 3.5-inch drives. The above drive has USB3 which will be of use when you replace the 2009 model, so the drive has retained value as your get newer computers.
We've had no issues with any of our OWC externals. That includes the older USB2 Elite on our 2011 iMac; it is now over ten years old and still happy.
I used "name-brand" mobile drives until they were getting in way of my work. Too many were designed to go on sale every other weekend, not to give long and reliable service. Yes, the OWC option may cost more but that issue is always settled when I ask myself, "What's my data worth?"
