The Second Meeting
Ask the designer to take the information from the first meeting and come back to a second meeting with specific ideas for your web site, a ball park figure for the cost of the web site, and a time line for completion.
One important area to discuss is web site development. The designer should have a process in place for web site development that allows you to see several designs in a testing environment.
Another area is what your responsibilities will be. Yes, you are a vital part of the web site development -- securing text and images, approving the layout, proofing pages, and giving constant feedback on site development.