Hi Allen,
You can make use of AppStateSerializer class in order to persist values.Please take a look at the sample attached and let me know if you have any difficulties to follow.
SampleSample shows the Loading and Saving of items under a button click event.Instead of this,you can use Form Load event and Form Closing event in order to Save and Load Selected items automatically.
Kindly let us know if this does not meet your requirement.
Best Regards,
Anu.