I think it depends on how much you are trying to sell your website for. I think as a frist step it would be nice to see traffic to the website year over year along with where that traffic is coming from. So for example, you could pull some aggregate data of a comparison of YoY traffic then have an overall break down of traffic sources for the last year or 6 months. In addition, to that data if it was me I would like to see engagement metrics like avg. session duration and bounce rate. It does no one any good if you can drive a lot of traffic but people are bouncing from the site and avg. session duration is very low. I am assuming they would like to see people are coming to the site and engaging with it appropriately. I would also include a breakdown of where website traffic is coming from geographically along with pageviews for each region. I think segmenting this out by Country would be appropriate if it is an international website however if you only deal with people locally I would just segment by state or region.
If you were going to hold off on showing revenue and financials then I would recommend pulling some backlink data from SEM Rush or Ahrefs. Also, I would consider showing some overall rank data from the site as well if you are actively tracking keyword ranking and positioning.
Then if they are serious I would consider going into Google Webmaster Tools (Search Console) and pull some data on the overall health of the website such as, the number of pages indexed, search analytics data like top queries or pages. At this point, I would show financial data and overall revenue of the website.
As a point of reference, I know Flippa lets you buy and sell websites. You can head over to their platform and navigate to the 'Buy' section of the site and see what sort of data other people are openly sharing about their websites.
Hope this helps let me know if you have anymore questions.