It depends. If it's a male singer, I focus more on the lyrics. Female singers can sing just about anything; I like the sound of their voices.

And obviously, I won't listen to a song if I can't stand the voice. There are some people who are like running a cheese grater across my brain - their voices are just that grating.

There's especially the sort? You know the kind? The kind that always talks in questions? Who just can't like, say anything else? And every other sentence? You expect them to say like yeah totally whatever? And then when they actually do it? You like, almost bust out laughing because it's just so stereotypical?
Sarah McLachlan - most of her songs that I listen to, I don't have the slightest clue what they're supposed to be about. And one of them, Touch, is all just vocal effects, no lyrics. Another one,
"Soul Sloshing" by Venus Hum is just gibberish to me, but I love Annette Strean's voice. It's unfortunate though that I don't like a lot of the music from their group, at least from what I've heard of Amazon's samples.
I also like the music to be calm or cheery. I don't care for the stuff that consists of guys yelling loudly about how they're constantly pissed off at every aspect of existence, and so are just going to scream into a microphone like an asthmatic howler monkey with brain damage.
"Australia" by Clarice - pleasant song. I have no clue what the lyrics are supposed to mean, but I like her voice. Alas, I also don't know where to find any more of her music, if there even is more.
Really, a lot of songs strike me as poems set to music. I can't stand poetry. Really really really don't like it. Back in school, reading poems, I'd just about read it with "Get. To. The. Point." between each line, then at the end, I'd "rewrite" the poem as a single, concise sentence, and marvel at the time wasted to say something so simple.