Who is the client and what does he/she do?
Do the services they need mesh with what you offer?
Do they understand the type of services you offer?
Do they understand your rates (and not question them)?
What are they looking for in a provider?
Do they understand your work process?
What is their communication preference?
Are there any hurdles that will be difficult to overcome (i.e. separated by several time
Do they seem to respect you?
What type of reputation do they have?
What is their general availability?
Do they have a sense of humor or are they all business?
What type of project is it?
What is their budget?
What is the timeline for the project?
Who is the audience?
What are the goals/objectives of the project?
What are the deliverables that are expected?
What are the expectations in terms of responsiveness and meeting milestones?
What are the benefits expected from this project?
What is the background on the project (is it brand new, was it started previously)?
Does the client have preferences for the project that you should be aware of?
Will the client want regular status check-ins?
Will there be any training, follow-up or support necessary after the completion of the
Who will be your contact person?
Who is the decision-maker?
Who else will you be working with?
More here. As a bonus, here are some red flags to watch for.
Hope that helps.