What criteria do you use when selecting outside counsel for litigation matters?

Not a particularly riveting answer, but we leveraged the recommendations of a (large) third party security provider to provide us recommendations in addition to our regular procurement processes. 

I trust the responsible in-house attorney to select counsel - they know the local legal market. I don't second-guess their selections. We consider qualifications and experience first, followed by cost. For significant matters, the firm’s brand name may be important. But for more routine matters, I'm comfortable with local law firms. I care more about the specific attorneys we hire rather than the firm on their letterhead. Large firms have deep benches, and that can be important for an urgent, complex matter. Of course, this is expensive.  But there are excellent attorneys outside of the big firms that are capable of handling most of our matters on a cost-efficient basis. It depends on what you need.