Man - read the DJ Bible.
But to summarize, a little of both. Sure you should play their song - but if you dig them, make it go something like this:
DanceHottie: Hey, can you play somesong for me?
SexyCleatDJ: Hmmm...yeah, I could play it. You like that sh1t?
DanceHottie: What?! Hey, that's not sh1t! That's good music!
You: I dunno...you'd better not be bullsh1tting me.
Her: I'm not! I can't believe you don't like it!
You: Alright, I'll play it but it had better be awesome. Don't go anywhere in case it sucks.
Her: Okay...
you play the song
You: (Act like your vibing it a little)
Her: So what do you think?
You: (put your hand on her shoulder and look into her eyes) Alright, this isn't too bad. I'll give you that. I'll tell you what. Why don't you give me your number and we'll talk about it some more.
Done deal.
You could also close by saying "I'll tell you what. Why don't you stick around till my set's over and we can talk about it some more."
Or, if you don't have time and just want to get her number, you could get it before you play the song by saying "Hey, give me your number before you leave - I'm gonna call you if this sucks."
Obviously I've never DJd so I don't know exactly what protocol is but it should at least give you a general idea of how you can play it.
~Sloopy