SSD are great! But consider the costs per MB and the remaining life of your system. Apple's newer OS's won't run on your system (macOS Sierra 10.12.x or subsequent versions), the highest it can run is El Capitan 10.11.x.
If you are planning on going with a small SSD then it makes more sense than getting the more expensive larger units given the age of your system. You might want to take a 1/2 step here going with a hybrid SSHD drive like Seagate's FireCuda It offers the speed of a SSD (cache) you're looking for here and yet has the depth of a traditional HD.
If you go with a SSD, yes you can get an adapter frame to support the smaller 2.5" SSD drive in the 3.5" HD bay. You'll need to transplant the thermal sensor over from the HD to the SSD.
As an alternative how about swapping out your optical drive for the SSD? That way you gain the benefits of getting the SSD as your boot drive for the speed and then leverage your current HD for the deeper storage. This way you also don't need to get a very large SSD (128 GB will do)
Here's the different IFIXIT guides:
Here's one frame you could use: OWC 2.5" to 3.5" Drive Adapter Bracket