THAT is the way to phrase the question.
According to the Wiki, the lowest tier to get the limited N is 490-778 and 50 minutes. Based on the math, the single R-Gacha seems to be the cheapest. A single pero glasses should do the trick, too.
No one knows how much burgers and shakes are worth. They have a point value that is known, but nutaku made an announcement that seems to indicate that she may give up limited cards more readily for burgers and shakes. I used a bunch of shakes and half shakes and got one of the cards (can't remember if it was the N or the R).