The 3 points you want to get across can be accomplished in just a couple of sentences that include (a) your announcement that you are quitting, (b) as of a certain date, and (c) provide information about your last day.
Why a Resignation Letter? In these digital times, why should we submit a resignation letter, anyway? A paper trail does seem old_fashioned, but in this case, it's a best practice. It makes your intentions clear, as well as the conditions. You're removing any ambiguity about the end of your time there.