For dtPicker you can use the dtPicker.Format to set it to whatever you want, including dtpShortDate and dtpCustom. If you use custom then dtPicker.CustomFormat can be set to any format (including "dd/mm/yy") however this will then ignore the users regional settings. Hence short date is probably the best choice for what you want.
As for storing it in Access, always store it as a date and then when you want to display it do the formatting. You should never store dates as strings in the database. Set the date format either in your SELECT statement or at the point where the data is displayed to the user.