2 Digit 7 Segment Display Driver
Options:


drive the segments directly from your uc. using the 200mA figure from the absolute maxima (which is strictly speaking wrong to do) you have ~ 14 mA per segment. You won't see the difference between 14 and 20 mA.
if you have the uc pins but want to use the full 20mA you can use two ULN2003 chips.
if you don't have enough uc pins you can go the 595 route. It has a total supply current limit of 70 mA (again: only mentioned in the wretched maxima section), so you have 10 mA per segment. Would be OK for me.
if you really want this display AND you have only 3 uc pins AND you want the full 20 mA per segment, sigh, you must go the 4 chips solution (or something equivalent, using a chip that is probably more expensive and more difficult to get).
ditch the display and get a more standard one with 2 anodes and shared cathodes (or the other way round), so you can multiplex. If you get a low-current version (use high-brightness displays that work perfect with 1 or 2 mA per segment) you can drive it directly from 10 uc pins.