In today's world of cut and paste, hack and slash web design many companies aren't finding the functionality or customization they wish for their website. Being annouyed with the "no coding required" website layouts is often too restrictive and cookie cutter looking to actually stand out in today's world. Maybe it's time to get what *you* want on a website. Designing and building a custom website will give you control of the functionality and style.
With that said, let's take a step back and realize that on any website "content is king". If you don't attract visitors with the site content, than you'll only please yourself with a fancy looking website. Make a list of what content you'll be offering, if need be break it into logical groups. Think about how often this content will be updated. If you're creating a website about the War of 1812, once the initial site is created it's not likely you'll be making revisions. On the other hand if your website is about stock market news, then you may be making changes many times a day and having a custom designed backend to allow easy site updates will greatly reduce the amount of your labor to maintain the site. These are two extreems, but it's to get you to think about how often and difficult it will be to make updates to the site content.