First a Solid State Disk (SSD) is just a newer type of storage it can replace your current Hard Disk (HD) but because of the higher costs per MB vs a HD many people use the much faster SSD as the boot disk and have second disk to hold their data content. That started the movement to setup a dual drive system.
Many newer iMacs have two ports to support two storage drives (2011 models onward). The older iMac's still can support a dual setup but one needs to give up the optical drive and the SATA port the optical drive uses is often a slower port so you can often encounter issues with it if your HD/SSD is too fast.
The hard drive vendors created a newer drive to help over come the dual drive problems called a SSHD. The hybrid drive is a standard HD and adding to it a SSD as a very deep cache. While its not quite as fast as a straight SSD it does overcome the problems of a dual drive setups in the older systems like yours as one does not need to remove their optical drive nor deal with the compatibility issues trying to get the SSD or HD to work off of the optical drives port. In addition one does not need to fumble with managing the OS and application files and moving the data files to the slower drive. Basically a Win - Win on both the hardware and software fronts.
So the best answer here is to exchange out your current HD for a SSHD. I personally recommend you go with a Seagate 3.5" drive.
But before you do anything:
Make sure your firmware is upto date. Follow this Apple TN on how to check and update it: EFI and SMC firmware updates for Intel-based Macs.
Then you should setup an external HD as a backup drive coping all of your important files to it. Then make sure your current HD is in good shape running Disk Utility from a second bootable disk. This could also be your backup drive if you get an external case to hold it (FireWire being the best as the older USB connection your system is very slow).