Pick and Choose Options

I have 8 employees. Each month I have opportunities for special assignments. The employees can select which opportunity interests them in an order they prefer. Based on who was selected last, last month, affects who is first in the next month. Anyway, I provide them with a calendar of the possible assignments. Currently, I just have a list of the assignments and they put a number beside the assignment showing which assignment they prefer and in which order. I would like to have the employee be able to click on the assignment in the calendar and have that assignment populate in a list in the order they choose their assignments.

I have searched many websites, read many how to documents, sat through numerous videos; but I have yet to even come close to anything like I am suggesting. So my first question is; is this something that could be done? If so, where could I research the background to make it happen? I don't mind someone providing me the results, but I really want to learn and don't mind researching the subject; but I haven't even gotten in the right ball park yet.

See attached. (I hope it is attached. I went to add attachments, uploaded and it says it's attached there. But when I close that window, I don't see anything on this window showing it is attached.)