Best ADC for EEG?

Thanks. I am trying to understand how to build an EEG.

AFAIK, the analogue pins on Arduino provide 10bit resolution, and I think I need 12bit or ideally higher. How can I do this?

Experiment with increasing the resolution for AnalogueRead [link]?
Or perhaps do the ADC with something else on the breadboard and feed the results to digital pins?

Sorry, if this is stupid. Thanks.