I continue to receive PMs and emails regarding my method of testing and selection of opamps, and the criteria that I use, so I will again explain the process that I use:
I first check the opamp datasheet for several specs- squarewave response, especially looking for peaking due to capacitances which can result in harsh or sibilant highs. I also check for slew rate, which is a measure of the "speed" of the opamp. Important for good transient response.
I then check for THD, voltage and current noise, and whether or not they are unity-gain stable and quiescent current draw.
If all these specs look promising, I then try them in a particular amp, using several known musical sources, interconnects, player, and phones. Several types of phones are always tried, both high and low impedance and high and low sensitivity.
In theory, all opamps suitable for our use should sound the same, as the audio bandwidth is a very small part of their total frequency bandwidth, and typically, distortion and noise are below the threshold that the human ear can detect, but we all know that this is not the case.
There are too many interacting factors inherent in the amp circuitry for the "theoretical" perfect opamp to actually sound "perfect" when installed in the amp, so it is a trial and error game to find that elusive sound quality that resembles a live performance. As an example, the LME49720 has about as close to perfect specs as one can find, yet many find the amp "overly analytical", "cold", "sterile", "tiring". So much for choosing by specifications alone!
It is important to mention here that NONE of the combinations I have tried sound really bad! I am simply evaluating them according to my tastes and preferences. I look for a weighty impact of fundamental bass, without smearing; for this, I use some recordings that include peals of thunder, recorded live. This is extremely hard for an amp (and phones) to reproduce in a lifelike manner. A sense of air around each voice or instrument is very important for good imaging, and highs that sound realistic, not harsh or sibilant. I listen to recordings that have applause in them, as that it a difficult thing to reproduce in a lifelike manner. Cymbals and snares tones are also a very good measure of transient ability and accurate high frequency reproduction. The voices of female vocalists are also a good measure of midrange ability, along with bassoon, oboe, cello, etc.
All amps are colored to some degree or another, even neutrality is a form of coloration. Very few live performances could be considered as "neutral" due to the surroundings, hall acoustics, etc.
One simply must pick the coloration that sounds best to ones individual tastes. I, myself, prefer the sense of realism that I hear when listening to a live performance while seated some ways back. I cannot ever recall sitting in the middle of the performance stage during a concert, unless, of course, I was performing, so I don't care for this feeling when listening to an amp.
The "perfect" amp will always sound like no amp at all. As they say, simply a straight wire with gain! Of course there will never be that "perfect" amp, but we are getting closer to the mountaintop all the time.
Bottom line is that my suggestions are based on my personal preferences in genre, musical setting, and most of all, that elusive, unmeasurable quality of realism.