If you want expandability, and to use almost zero Digital I/O pins for the purpose of merely LED driving, think about using a proper LED driver chip. You can do schenanigans with shift registers, but you will only go so far. If you are going to invest in board space for these ICs, why not just use a good old I2C bus LED driver with 16 channels each? Like the TLC59116 by Texas Instruments
Four hardware address pins allow up to 14 devices on the same bus. That gives you 14 * 16 total LEDs, all individually controllable (open drain, you can connect them straight to the IC with resistor from your voltage rail (up to 17V rated too!)
Not only are they individually controllable, but because it's an I2C bus you can add/remove any device from your "motherboard" in a very easy way (power + I2C connector, done!). Up to 224 LEDs with 8-bit PWM dimming, bus-wide commands, or individual LED commands. Quite amazing. Try it!
I should point out that by all means, try other types of multi-channel LED driver ICs, however the fact that there are I2C bus compatible ICs out there makes them EXTREMELY useful for expand-ability and quickly add/remove large amounts of LEDs, merely changing some software to deal with the hardware changes. The ICs are fairly cheap, only a few $ each but they will be better than trying to administer to many shift registers as fast as possible - let an IC deal with it, because that is what the are designed for.
Finally, you may use these more for "logic" than actual power driving, if the LEDs you are trying to drive are heavy duty (like, hundreds of mA to Amps each) by using inverting buffers and push/pull totem pole (also called cascode circuits) to operate the gate of a MOSFET (usually N channel, in a low-side power switch circuit).
If each individual LED draws less than around 50mA you can control them with a series of 74HC595 shift registers and ULN2803 darlington drivers (one series resistor for each LED).
You'd need 10 of each of the chips and 75 resistors (total cost = cheap). You simply shift data (bit high= on) and then transfer the data from all 75 to the output latch. If you want you could transfer data in parallel into each channel which would be faster. You can use a standard NI digital output board and one of their uber-expensive cables + breakouts.