There are plenty of SSD options for the Late 2012 iMac, ranging from easy and cheap, to very fast, complex, and expensive. You can use SSDs externally on the Late 2012 iMac with USB-A, USB-C, TB1/2, TB3, SD Card, and even FW if you want.
You are probably looking to get the easy and cheap method, which is a simple 2.5" USB3 enclosure or adapter cable and a SATA SSD. This would give you speeds around 450MBps.
New Egg has a 2TB SATA SSD for $130, with good reviews:
Buy Team Group EX2 2.5" 2TB SATA III 3D NAND Internal Solid State Drive (SSD) T253E2002T0C101 with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com
You can always spend more for a Samsung or something as well.
I like this adapter cable because of the longer cable than others, for $12 on Amazon:
Product Description:Take advantage of the lightening speed of USB 3.0 to quickly transfer files up to 5 Gbps! Connect any 2.5'' Serial ATA (SATA) / SSD or SATA II Hard Drive to your computer through an available USB 3.0 port on your desktop or laptop. Reverse compatible with USB 2.0 and 1.1, this...
www.amazon.com
If you would rather have an enclosure, they are usually about that same price as the adapter cable I posted, about $15.
You can get more expensive USB3 SSD drives, such as a Samsung T5, they are good drives, but more expensive and not any faster than buying a SATA SSD and USB enclosure or adapter cable.
If you are looking for more speed, you can get a TB2 SSD. They are expensive and not a lot of options, but you would get about 700MBps speeds.
You can get even faster using TB3, 900Mbps+, but this could require more equipment, such as a TB3 dock, and probably not worth it for what it sounds like you are looking for. You can also use the USB-C ports on TB3 docks and run them at the higher link speeds if the drive and port on the dock is capable to run at higher speeds.