Generally you would use some form of regulated excitation and a signal conditioning circuit with trim for bias and gain and and some reasonable frequency response for the intended application.
Since the input signal is differential, an instrumentation amplifier is typically used.
Since the input signal is relatively low level, often a "zero drift" or "chopper stabilized" type is specified. The load cell itself has drift both with temperature and with creep. Applications like scales where the scale is zero'd prior to measurement and then the load is applied for a short time can get away with less precise circuits as far as bias drift goes.
For consumer applications, a part such as the Avia Semiconductor (Xiamen, China) HX711 is sometimes used, which includes excitation, analog front end with PGA (programmable gain amplifier) and high resolution ADC converter.