Current Sensor Resolution
I'd recommend the ACS722 10AU sensor. However, you will likely not get the accuracy you want from a Hall effect device. A shunt resistor is always more accurate, but that comes at the cost of BOM lines and potentially more expensive amplifiers/current shunt's (at least at the very good sensitivities/very high currents). The integrated Hall-effect current sensor market is reducing module sizes and BOM cost by making compromises on total accuracy. If it works for your application, great, otherwise use a shunt resistor.

The bandwidth figure you see is the maximum current frequency the sensor can resolve.