What do you mean by sincerity? pick a pretty girl (or girls) and have them give you a dance. If a girl you're not into asks for a dance, say no thanks. I don't see what's so difficult about this. Also, I'm kinda bothered by you being bothered that some girls are there for rent money. News flash: even the dancers who absolutely love their job are there for money as well.

And as for drink prices, yes it can be expensive, but most places won't hassle you all night about buying another drink if they see you buying dances or at least tipping on stage. Just nurse your drink.