chosing the right Hall effect sensor
You should use a sense resistor and a current sense amplifier -- this will give you far superior accuracy to either a Hall effect sensor or an instrumentation amplifier.

The LTC6102 is an excellent current sense amplifier. Its maximum offset voltage of \$10\rm{\mu V}\$ permits great accuracy, but it can only sense current in one direction. If you need to sense bidirectional currents and are willing to live with a bit more error, the LT1787 is a good choice, with \$75\rm{\mu V}\$ of offset.