The Mega has lots more pins, and is perhaps the simplest solution.
Now that good MEGA copies are close to $20 it makes sense to use it instead of various expander approaches. And you also get 4x the memory!
DISCLAIMER: Mentioning stuff from my own shop...
MEGA example HERE:
and to make connections to all those pins much easier, add a MEGA Sensor Shield:
How-To about Sensor Shields HERE:
Cables and Connections HERE:
MEGA details HERE: