Rotate through views result weekly
Add a date field to your tip of the week content type.  That date field will indicate when the tip becomes visible on the site.  Order your view by date (descending), and filter out all entries where the date field is greater than the current date.

If you want to write some code, you can add a hook that runs when you submit the form, and, if you leave the date field blank, have it select the maximum value of the date field out of the database, add a week to that, and fill the date in automatically.