How much does nipple choice affect wheel weight/stiffness?
Alloy would save a tiny amount of weight. I wouldn't expect it to make any difference to wheel stiffness, so long as you lubricate the threads when building it (alloy nipples are stiffer to turn otherwise, so it's harder to get the tension right). Brass is stronger, but you shouldn't have to rely on that to get a stiff wheel.

But long term, alloy is more likely to seize.

http://sheldonbrown.com/wheelbuild.html#nipples

http://singletrackworld.com/forum/topic/alloy-spoke-nipples-or-brass