Which one is the better way to feed analog input to my ADC?
The ADC will handle +/- 80 mV signal BUT needs the proper power supply to do so. 

One "naughty" but entirely valid way of getting a small negative supply is to place a diode in the -ve return power supply lead.   

System ground including all regulators etc are at the true ground = anode = most positive end of the diode and - 0.6V or so for a Si diode is at the cathode.   

A Schottky diode gives a lower voltage, that may be enough here. 

Place a decoupling capacitor across the diode.  

Vin- will vary somewhat with overall system load and decoupling (here = C1) needs to be adequate to avoid secondary effects. 







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