How to choose current sense resistor and current sense Amplifier for precision sensing
You start by asking your self how big in value you can make the resistor. The bigger the value the easier it is. For instance, if the resistor is 10 ohms then 500 mA produces a volt drop of 5 volt and a lot of ADCs will work with this sort of level and you won't need an amplifier. With 16 bit resolution you can resolve a current step as low as 7.6 uA so your lower limit of 10 uA resolution seems OK.

However, 10 ohm at 500 mA does "lose" 5 volts and this may be far too much for what is connected as a load. So, you have to decide how much voltagee you can afford to drop. If this is 0.5 volts then the current sense resistor MUST be 1 ohm and no-more.

Then you would need an amplifier with a gain of ten to feed your ADC.

But, remember that the lower and upper 50 mV voltage limits of any ADC are likely to be problematic in that zero offset and gain slope variations may make these areas unusable from device to device so, you need to read the data sheet and decide how low your ADC can get before it hits the end stops. If it is 50 mV above 0 volts then current measurements below 1% of 500 mA might not be reliable.

Bear also in mind that resolution is definitely NOT the same as accuracy.