My suggestions:
1. Make sure that anything you wish to keep has been saved to your new computer.
2. Create new accounts for your parents. These can be "regular" (non-administrator accounts), or you could give them administrative privileges. What you decide depends on how savvy your parents will be in regards to administrating the Mini.
3. Create AN ADDITIONAL NEW ACCOUNT with administrator privileges. I suggest you give it an obvious name, such as "administrator". Also, give it an easy password, like "mini".
4. Now, restart and boot yourself into the "administrator" account.
5. Next, DELETE your old account (the one that was yours up and until this time). You will have to choose whether to "archive" it, or fully delete it.
At this point you may want to re-check and make sure all your personal data has been removed (may have been located in places other than your home folder).
You might want to launch Disk Utility, and tell it to "zero out" the "free space".
Finally, set up the "users & groups" so that it will boot to your parents' account.
Now it's time to hand it over to them.
Additional notes:
The reason for the additional administrator account will be for YOU to use, if you ever need to do "tech support" for your parents.
If I was prepping a computer in this manner, I would also run something like "Yasu" on it, to "clean everything out".
Also, the very last thing I'd do (after Yasu) before handing it over, would be to boot from an external source, and defrag and optimize the internal drive. This will group all files at "the head end" of the hard disk, and leave one contiguous area of "free space" behind it. A good way for them to "start clean"...
