Get the max7219.
74ls/hc595 can be used (both are much faster than needed for displays) but neither chip is a good choice for displays because their current capabilities are low, especially if you are multiplexing. These chips are general purpose logic chips and were not designed for displays. If you used them, you would need more components like series resistors for the segments and transistors for the digit connections on the displays. Also your code becomes much more complicated because the Arduino must perform the multiplexing.
By contrast, max7219/7221 was designed especially for displays so has a higher current capability, minimises the number of extra components needed and keeps your sketch simple by performing the multiplexing so that the Arduino does not have to do this.