Normalised Current Transfer Ratio of Opto-Coupler
What calculation do I need to use to determine the required resistor
  on the LED?


Sparkfun has a good tutorial, you'll need figure 7 to find the current/voltage relationship 


  Also, how can I determine what resistor on the LED can deliver the
  most current?


The diode curve is in figure 7. 15mA equates to 1.2V on the LED at 25C. 

If you look at the CTR for 5mA, figure 3 suggests that there would be 1.2 for the CTR and the transistor would see 6mA. This only holds true if the temperature is kept at a constant 25C.

The CTR varies as much as 40% across the range with temperature, so this needs to be taken into consideration. 

This is how I would find out how much current I can get through the transistor with figure 3:

With the LED at 20mA I have a CTR of 0.6

0.020*0.6=0.012 or 12mA

With the LED at 15mA I have a CTR of 0.8

0.015*0.8=0.012 or 12mA

In both cases the transistor has saturated, which is probably why the curve goes down as the LED current goes up.