About them
Where is the money coming from, and is it committed? What else do you own, and may I speak to those sellers? How long do you intend to hold this business? Have you ever run something like it?
A buyer who cannot answer the funding question plainly is not ready to buy.
About the business afterwards
Who will run it day to day? What changes would you make in year one? Will the name stay? Will the site stay? What happens to my longest-serving staff?
Ask for the honest version. A buyer promising that absolutely nothing will ever change is either naive or managing you.
About the deal
What does the offer consist of, and what could reduce it? What do you need from me after the sale, and for how long?
Write the answers down. The gap between an early conversation and the final contract is where disappointment lives.