What should you be looking for when starting a new website:
Make it easy to navigate, less clicks is better.
A good lay-out will make your website more accessible and readable. Columns (wireframes) and white space are very important elements.
3. Graphic elements
Make sure the graphic elements fit the purpose of the website.
Colors (together with some other elements) will determine how people perceive you. Study them carefully and make sure they match...
Same as above, your typeface will inform your visitor of who you are, and determine the readability of the website. Less is more in this case.
The purpose of your website (information sharing, selling, ...) will determine all of the above.