How to measure supply currents ranging from 1μA to 10mA?
If you want the average current and the high current peaks are brief you can parallel a higher value resistor with a capacitor such that the voltage does not drop excessively. You could parallel a higher value resistor with a Schottky diode (to get low current measurements without impairing functionality) and make separate measurements of high and low current. Those methods have been sufficient for my purposes. 

Shopping questions are off-topic here, but Dave Jones of eevblog notoriety does offer a product for this purpose. You could even build it yourself since he publishes the schematic, but buying it makes more sense. He uses low value shunt resistors and a very low Vos amplifier.