Trade offs between adc range and amplifier gain design
I think... the more you amplify a signal, the greater the distortion and extraneous noise you're likely to introduce. I'd use the lowest-range ADC I could reasonably muster, so I could use the lowest-gain amplifier to match it.

Less introduced noise means less noise to dispose of later.

Use the highest-resolution ADC as you are prepared to handle the bits for - if you're only prepared to deal with 12 bits, only use a 12-bit ADC. Nothing is gained by throwing away bits. Some higher-resolution ADCs, too, require more sampling time than their equivalent lower-bit-count cousins, so if you're crunched for sampling time (need to sample often), a lower-resolution ADC may actually serve you better even if you lose the least-significant bits.