I was going through Starting Strength and some other forums on this and was not certain. But what exactly constitutes a good bar speed for the Squat? And would this be the same for other movements as well?
Depends more on what you're trying to accomplish than the movement itself. I squat as fast as possible most of the time because the reason I squat is to clean better, and the clean recovery is quick.
If you have nothing specific to work for, I would suggest a "natural" speed. That is, do what feels good to you. At least some of the time, though, try to accelerate through the concentric phase as much as possible to get some more power development in addition to strength.