How to create Most Commented and random category

I have arras theme with this i can add to home: posts by category, by taxonomie or all post. I want to know if there is same way to create a category (or taxonomie) with all post and when arras put this category in home, home show me in order from which have more post to that have less post.

And if is possibile i want to know the same thing with random order.

Thanks