what transistor should i use?
One suggested option that involves no code or design changes, no transistors, and just one resistance calculation:

Replace the 74HC595 in your design with Texas Instruments TPIC6C595 shift registers instead. These are higher current versions of the 74HC595, supporting up to 100 mA per output pin. They use power DMOS transistors for the output stage, instead of low current elements. 

The same family also offers TPIC6A595 for 350 mA per channel, and there may be similar power logic shift registers from other manufacturers as well. 

All you need to do then is add a resistor in series with each LED, computed in value to limit the current to what your LED requires. 




See Correct formula for LED current-limiting resistor? or How do I calculate the resistor value for a simple LED circuit? on this site, for calculating a suitable resistance.
See Why exactly can't a single resistor be used for many parallel LEDs? for an explanation of why wiring the LEDs in parallel without separate resistors is a bad idea.