For a website are there parts of it that are more important to track than other parts

Well to be honest the most important pages to track are your money pages. But you should track all pages of your website to see what is being used by your visitors. This will provide huge insight into what your visitors are most interested in.

Armed with that information you can give them more of what they want. Using analytics software like Piwik analytics or Google Analytics will help you identify which pages are most popular. You'll see which keywords are being searched for, other web pages referring your site, and lots more to help you understand what your market better and how you can give them more of what they want.

Providing more of what your visitors want keeps them on your website longer, this makes the search engines happy and allows you more of a chance to make the sale.