I need to figure out what voltage and current range I would need to measure to within 4.8Ω (= 240Ω * 2% I assume I did that right).
it will depends on how you measure it.
How would I calculate my resistance measurement accuracy?
Again, that's a function of how you measure it.
if you have access to high precision resistors, a ratio-metric approach would be good. it doesn't require a high precision current source.
The simplest ratio-metric approach would be an adc that takes differential reference inputs. Put your high precision resistor across the reference voltage inputs and you are ready to go.
if you have to adc the voltage across your resistor, you want its minimum resolution to be at most 2% of the voltage drop. For example, if your current is 1ma, and 4.8R -> 5mv. With a 5v Vref to a 10bit adc, that works, barely.
Typically the last 2-3 LSB of an adc are fairly noisy. So in that case, you want the resolution to be 15mv (= 3 * 5mv) on a 4.8ohm resistance. that least to a minimum current of 15v/4.8R = 3mv.
You will then do the same calculation to make sure that your adc doesn't max out at the top end of your adc. Or you potentially need to switch Vref dynamically or switch to a higher resolution adc.
but the basic thought is there.
the questions have nothing to do with 4-wire measurements.