I would just play the one you have to be honest, the sequels are really more of the same (though I haven't played Origins). That's not necessarily a bad thing though, I personally enjoyed Asylum, especially the fighting combo/counter system.
If you enjoy Asylum then you can pick another one up later. Arkham City was released a fair while ago so I imagine it could be picked up fairly cheaply in the future outside of a sale.
Otherwise said, if you buy City and Origins and then find out you don't enjoy Asylum you're triple stuffed!