Personally El-Aurians have always been one of my favorites, younger writer me liked peppering those several hundred years most have under their belts by the time they join Starfleet with colorful events and a bit of mystery. The mystery surrounding their abilities as 'listeners' and their preternatural knowledge of, but-not-limited-to shifts in the space time continuum always adds a nice POV element. Their worldview must be pretty different, especially if they possess extra senses that we do not, which sometimes makes it hard to write (usually why I stay away from true telepaths) but is ultimately really rewarding as you try and think about their perspective and what informs their perceptions. This is where a lot of creativity comes in if you're playing a species without a lot of background or screen-time. Personally I love putting my anthropologist/sociologist hats on and thinking about what their societies must be like. Even something as basic as naming is pretty interesting. Across the world most Human surnames are patrilineal but Tahlin's surname isn't his father's or his even his mother's so where does it come from? I haven't entirely worked it out but the idea I have in the back of my mind is that El-Aurian surnames are complicated things that don't follow strict or familiar conventions as evidenced by the portrayal of both mononymous and polynymous individuals.
And I think generally that's the kind of mixture of set variables, like what we see on screen or in books and the freedom to suppose or just entirely make up little bits for ourselves, that I personally look for when choosing a species.