Good news. And the display?
While you're waiting for those max chips, here's how you should wire an led display directly up to an Arduino.
Notice there is one resistor per segment. One per digit would be incorrect, because the brightness would not be consistent between say a "1" and an "8". This is because of Ohm's law.
Also the digit lines each have a transistor to take the strain off the Arduino pins. For the segment pins, you can get away without transistors because each Arduino pin only has to supply current to one segment. But for the digit pins, the Arduino might have to supply enough current for 7 or 8 segments, which would go over the maximum (40mA). You could use higher series resistors so that this current stays under 40mA, but that would make the display quite dim. But the transistor amplifies the current, so that the Arduino pin only has to deal with a few mA, but the digit gets as much as it needs, e.g. 160mA.