20 mV seems like way too much ripple for an LDO.
Having a separate regulator for your op-amp is a good idea here. The op-amp should ideally have its gain set so that your 80 mV full scale reading is around 80% full-scale on your ADC, so you shouldn't have a problem with leading zeros. In that case, one LSB will be around 25 microvolts. This isn't a terribly small number, but it is enough that you need to put a little care into noise if you want maximum performance. Op-amps have fairly good power-supply rejection, at least at low frequency, but it is always best to start off with a quiet supply.
I wouldn't use voltage references as power supplys as a general rule. They can vary quite a bit in behavior, but they work best as references: with a small, constant load. Use the reference for your ADC reference, or for a virtual earth if necessary, but any linear or LDO regulator should perform fine as an analog supply as long as you follow the recommendations for capacitance.