The problem you face is the hard drives SATA port is only SATA I (1.5 Gb/s) in your system. You'll need to find a SSD which can run at this slower speed. Sadly, I don't know of any newer units that would work. Most are SATA III (6.0 Gb/s) and might drop down to SATA II (3.0 Gb/s).
The other issue here is you'll end up still needing more traditional disk storage (HD) as the larger SSDs are quite expensive.
How about a half step here: Instead of putting in an expensive SSD go with a SSHD hybrid drive like Seagate's Desktop SSHD. That way you gain the speed benefit of the deeper SSD cache the drive has and still hang onto the deeper storage of a traditional HD as well as being cheaper >> a Win - Win !! <<
This drive also runs at SATA I so it will work in your system as well. Most HD's now are SATA III and won't work in your system. I would stick with the 1 TB drive.
The last issue here is making sure your systems firmware is up to date. Follow this Apple T/N: About EFI and SMC firmware updates for Intel-based Mac computers