Use a current monitor IC or roll my own?
You can build one with a simple op amp circuit, but it will take more design work, more external components and likely more board space.  There really isn't a reason to do so unless you have specialty application which requires something out of the norm.  

Current monitoring for battery powered devices is a very normal application.

There are current monitors out there that output a PWM signal that you can monitor instead of a voltage that to be read with an ADC.  This type of monitor may be easier to interface with and require less power to monitor depending on the type of microcontroller your using and available peripherals.  You can also get regulators with built in current monitoring circuitry which can reduce part count, cost, board size, power usage and increase accuracy in some applications.