What is the correct method to display a large popup menu?

I browsed around a little in the documentation, and instead of using popup.append(new_menu_item) you could use popup.attach(new_menu_item, left, right, top, bottom) to put your menu items in a grid instead of one long line.

But it seems like you would be better off opening a window with a scrollable list, though!

Use a GtkComboBoxText. But as ptomato said, this kind of presentation isn't adapted to lists of a huge amount of values. Either reduce the number of values to show, or use a GtkTreeView, which will have a scroll bar and won't need an initial click to show values.