Sounds like an involved robot. Parallax has alot of robots, but not a stair climbing robot to my knowledge.
Parallax has a balancing robot, which may help on your way to making your robot. Programming, or
coding, will depend on the complexity of the robot. If you have most of the gyro programming out of
the way, (as provided by other programmers) then you can proceed to develop your new code, as
required with your new robot legs/system.
I would pick a microprocessor that has support for its editor, debugger, and terminal programmer.
You are going to need all the code "snippets" that you can get. Motors, sensors, drivers, bearings,
metal supports, and accessories will have to be taken into account when programming; because
mechanical adjustments make a difference in radians, in reference to your PWM motors.