Ask for concrete deliverables
Separate discovery, design, content, development and ongoing work. For each part, ask what you receive, who approves it and what counts as finished. “Improve the website” is harder to evaluate than a named set of pages and acceptance checks.
Choose evidence you can inspect
Ask the provider to explain a relevant example and their role in it. Discuss how they test forms, mobile layouts and the move from the old site. A useful answer shows a repeatable process without promising a particular commercial outcome.
Discuss the months after launch
Clarify maintenance, ownership, access and the cost of future changes before work begins. Agree where issues are recorded and how priorities are set. Keep a written record of assumptions so a later change can be discussed against the same brief.