Although I don't have enough exposure or experience like some of the more seasoned audiophiles on this site, nonetheless I have gone through 10-12 integrated amps (tubes and SS) in the last 5 years. There are a few sound quality attributes that I have come to realize that I prioritize over everything else. But if I have to describe it in a single sentence, it will be "thou shall never ever sound lean!"
And it's precisely for this reason I keep going back to tubes.
Let's share your top priorities in a single sentence :)