Arduino remote shutter for DSLR camera - need help with choosing right resistors

There is no reason to provide a pull-up resistor on the Arduino, especially if you are referencing the optocoupler to ground, as the pull-up would then tend to turn the optocoupler on until the Arduino pin is defined as an output and set low.

390 ohms sounds perfect. I suspect 470 and even higher would do just fine.