I managed to get two base pieces of the set and 8 selection kits. I didn't follow any particular strategy and even started a day late because I didn't know there was a mini-game involved. I didn't try to complete every task - if I saw it would take too long, I skipped it. I tried to save Pots of Gold and not spend them on the mini-game too much. I didn't use Pots of Gold to get items after completing each city, only taking the freebee.