Personally, I'd like to work with a younger faculty member who has just received tenure but it still looking to further their career and depending highly on motivated graduate students. Sort of a cheap way out, but easily the most ideal.
I think too old, and too established groups are easier to get lost in, and I've heard horror stories about being a disposable worker and never have a good connection to the faculty member who will be writing you a very personal LOR once you graduate.
It also scares the hell out of me to pick an assistant professor with some awesome research, only to have him/her leave in the middle of my studies and leaving me struggling to stay afloat.