The joists run the 12 ft direction, from the ledger out to the beam. This plan uses 2x8 at 16 in on center, which span 9'-11" against 11'-10" allowed in the DCA6 table for Southern pine. Move to 24 in spacing or a longer run and the table asks for a deeper joist.
The 16 ft side does the rest: the beam is split over 3 posts, so each beam span is only 7'-0" and a 2-ply 2x10 beam is enough. That is the trade you can make in the designer, fewer posts with a heavier beam or more posts with a lighter one.
Materials come to at least $2,490.97 at Home Depot prices, with 28 5/4x6 pressure-treated wood boards, before tax, delivery and labor. For composite decking, change it in the designer and read the new list.