The Sound.
(To my ears).
And aesthetics.
I have certain things that I value in sound reproduction, hence in the ways speakers can sound. So i’m not chasing numbers (measurements) per se (not that those are inconsequential of course), but rather a sound I want.
When I encounter a speaker that does more of what I’m looking for, at a show, a dealer’s place, another audiophile’s system etc, ...that’s my criteria. I will however be put off if I find the speaker to be ugly. I also want my speakers to be a nice piece of furniture. Fortunately there are so many speakers out there, finding a combination of pleasing sound and aesthetics hasn’t been impossible.
Outside of my own direct encounters with speakers, I will also look to things like speaker reviews, the reports of other audiophiles, to suss out whether people are hearing positive things I care about in a particular model. So for instance all the reports of the textural presence and sonic weight to the sound in the Devore O series speakers ticked some of my boxes, which led me to seek out auditions. And indeed, they ticked those boxes.
Where with my Joseph speakers, I wasn’t led to them via reviews, but by a chance encounter at an audio show. I wouldn’t have necessarily known they stood out for me, unless I’d heard it for myself.
I’ve found my long term CJ Premier 12 monoblocks have been happy to drive speakers big and small, "hard" or "easy" to drive, in my room. So although I favor tube amps, I don’t feel I need to seek out speakers specifically "tube amp friendly."
One thing though is that I can be very intrigued simply by the looks or design of a speaker. It may be the aesthetic beauty, or the audacious or idiosyncratic quality of the design, that makes me feel "Man I’d love to hear what that sounds like." That’s one thing I love about the variety of speakers at audio shows.