I noticed on their website that a promotion must be selected from the
dropdown menu. The choices are either the membership card guided tour,
or the promotion membership card. For the membership guided tour,
there is the option to purchase a number of tickets. For the promotion
membership card, the only option is for one ticket. I need to get two
tickets. It seems like the membership guided tour might be best.
Laurie, no, you don't have to choose a promotion. You only do that if you're, say, a holder of the membership card. That card only makes sense to purchase if you're planing to use it many times over the course of its 12-month life as it's much more expensive than one-time tickets or tours. So just ignore that dropdown and go straight to the ticket options once your date comes up as available. If you're wanting a tour, scroll down the ticket options for that date to any available "ENGLISH GUIDED TOUR" slots. The price will be €25.00 per adult. Otherwise just choose the standard adult ticket option.
Editing to add: that ticket price may go up after the renovation is done and the works temporarily moved to Palazzo Barberini are back in place. That deadline has already been moved out once, and appears to have been moved out a 2nd time to Oct. 27th.