Playing Arkham Asylum first is a good idea, not just for story reasons but because it is a fantastic game in its own right.
And after you play it, you'll be able to appreciate City all the more because it is one of those rare games which proves itself to be a true sequel and it builds off basically everything the original had.
Although IMO the Arkham Asylum suit>>>Arkham City's. It's just an aesthetic thing, but I prefer that black leathery look to City's bluish cloth apparel. And the battle damage looked better in the first one as well.
The world is cruel. And the only morality in a cruel world...is chance. Unbiased. Unprejudiced. Fair.