What aspects, other than actual legal issues, do most attorneys consider when consulting with a potential/new client for the first time?

Question Details: I ask this question in order to find the right attorney for my case. I've wasted a lot of time myself and perhaps of those I have already consulted with unintentionally simply by not considering and/or knowing what matters in the first consultation for attorneys who meet with potential clients. For the kind of answer I seek by asking this question, lets assume that a new client has cause and legal facts are just for a lawsuit.

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