The extra bits are useful if you want to do averaging. They are not meaningless, they are just in the noise. A 12 bit with 10 ENOB is better than a 10 bit with 10 ENOB.
Not to beat a dead horse, but what is your requirement again? I thought you said you wanted 12 bits and 10.5 ENOB which is reasonable and many parts deliver that. I guess I'm not sure I am helping at this point... 8*
There are other tradeoffs than just speed. You can run fast, accurate or low power... pick two. I think we are agreeing on 12 bit with 10.5 ENOB. But I think you said somewhere that you wanted *more* than 1 MSPS and/or you were going to average the samples.
No, I don't think it has to be Gaussian distributed, but maybe it has been too long since I used any of the theory. I believe the basic assumption is normally that noise is Gaussian, but in this case it only has to be uncorrelated. Does that imply Gaussian?
Yeah, that is what I am thinking. I guess you started out asking for practical advice and this turned into a discussion of theory. The best answer I can give is the ADI ARM7 microverter parts. They have the best ADC/DAC in an ARM MCU that I am aware of. I think someone else already mentioned these parts. They are only so-so in the MCU department, at least in terms of speed. But speed is not always what a design is about.
You can see an older comparison chart of some ARM7 devices at
Rick