Answer: Marc-Andre Fleury.
This is kinda a no brainier. He is all ready the public face of the organization. As a three time Stanley cup champion he has more experience then anyone else on the team. I am also going to put this out there, as of right now he is the 15th overall in wins for a goalie. He has been a steady force in goal for the Penguins for over a decade.
Wait...A goalie as captain? Yes! Roberto Luongo was captain for the Canucks. Yeah, so Luongo doesn't have any cups, but he is 5th in overall wins!
Question: Who should the assistant captains be?
Answer: James Neal, and Deryk Engelland.
Yup, you read that right. All three former Penguins. They all played on the Penguins in overlapping seasons. The James Neal who I remember helped Malkin get the Hart trophy in 2011-2012 season. Meanwhile, he helped himself to a career high of 40 goals that season. He also wore an "A" while playing for the Predators.
Why Deryk Engelland? He is one tough customer. At 35, he adds a lot of experience.