A pH sensor outputs an analogue voltage, so you can't measure it in bits.
The correct ADC depends on what resolution you want.
Say you want a resolution of 0.02pH, with a range from 0-14pH. Then you need 14/0.02 = 700 discrete steps, which is log2(700) = ~9.45 bits. So a 10 bit ADC would cover this, giving you a resolution of 14/1024 = 0.0137 pH.
How precise or accurate the readings actually are would depend on various factors, so it may be pointless to go for more bits unless you can actually make use of the extra resolution.
EDIT - If it's just a passive sensor, you can't connect the sensor directly to the ADC, as the output impedance will be very high and the ADCs input impedance will be low in comparison, so it would load and attenuate the signal too much. Also you need some gain to match the sensor output voltage range with the range of your ADC.
What you need to do is use an opamp with a very high input impedance (e.g. FET input type) to buffer and amplify the sensor signal before it goes into the ADC.
However, the fact you mention 4-20mA output makes me think your sensor may have an opamp on board already, in which case you may be able to simply connect directly to your ADC.
To confirm this can you provide the sensor type and model number if possible, and the voltage range on it's output (plus any other info you have about it)
Also, how you are planning to send the ADC data to the computer (USB? Serial/Parallel?)