Would the best method be to install the OS on the SSD and then keep all my files on the HDD?
What do you think is the best way to partition my installation, and how would I do so?
Basically, This is more about how you use your system. Since you have tagged your question with "dual boot", I consider you will have Win7 or Win8 as your second OS. If you do not intend to use Ubuntu as your primary OS or do not want to install too many games/softwares then meeting the minimum Ubuntu Requirement+3GB on SSD will be enough for you.
Note, Software like Browser (Firefox) office suite (LibreOffice) is already included in the minimum requirement. In my opinion 10GB will be more than enough.
Windows8: 16GB (min. requirement) + 6GB-10 GB (for user files and software) Ubuntu: 5GB (min. requirement) + 3GB-5GB (for user files and software)
You should install softwares to HDD, which you don't use regularly or need storage in GB. Also move all user files like music, docs to HDD.
Here are the 2 cases I that I have tried when using an SSD and an HDD:
Windows + Ubuntu Case - I am assuming you have Windows on the SSD which is taking some part of the 32 GB space and the 500 is used to store other files. So the best thing would be, if you are able to get from the SSD at least 8 GB to 16 GB is to install Ubuntu in the SSD (Share it with Windows) but since you will only have a small amount of space, you will need to either start moving heavy files to the 500 GB HDD or to set the
Ubuntu Only Case - If you only want to use Ubuntu, then install it on the SSD for the same reason as the Windows + Ubuntu scenario. The speed that the SSD will offer will save you time when booting, loading system files and more. Of course 32 GB is not much if you start downloading huge files but then again, you have enough space left to move files to the 500 GB whenever you feel you have little space left.
The benefit in general of having the root filesystem