The simplicity or complexity of the web site generally determines the price. A few buttons with simple screens of text will demand very basic web design skills. Lengthy, complicated sites require more skill and time on the part of the web designer. Be sure to request an array of sites that display a cost range from less to more costly. Ask what browsers will support the designer's sites.
Different browsers support different site features.
The latest edition browsers will respond to the latest bells and whistles. On older browsers, these same features will slow the download time and may even cause them to crash. Ask about the design process. Get a sense of their working style, their adaptability. Once the site construction begins, an exchange of ideas and suggestions from both parties marks a healthy process.