Time Machine: should I partition a 500GB disk?
Technically you could do this, although 50 GB is far too small for most any use these days. 

The point of concern I think should be raised here is that you look to be hosting both files and backups on the same drive. When (not if—when) the hard drive fails, you will lose both. You would be much better off in the long run keeping the files and backups on separate drives.

UPDATE (based on comments): The rule of thumb that I've seen for deciding on a drive size to house a Time Machine back up is at least a 2:1 ratio of the drive to be backed up (so a 500GB would mean a 1 TB TM-hosting drive), and I don't see why that general rule couldn't be followed here. 

Look at the data volume of the folders you intended to back up, double that, and that's the size partition you go with. If Time Machine requires a minimum that's below what you calculated, just double the size of that for your partition and off you go. 

Either way, I don't think you're going to find a hard number here.