This misconception is the ruin of many websites. I see many examples of websites where there was initial concern about the graphics, and it looked beautiful, but their information is old. This happens because a web designer was hired to get the website it up and running, but the maintenance was not planned out.
A common example is a neighborhood website with updates that don't get updated. For example, the fictitious town of Smalltown U.S.A. Today is March 5th, but their pretty main page asks the reader to "Get Ready for The Biggest Event, happening February 25th!". Pretty page; old content.
If your content is old, then a pretty website won't get you far. Don't get me wrong: attractive graphics are important. But if your goal is to have timely information updated, you need to have that aspect secured in your initial strategy. If your business is a one-person operation with very limited time to make updates, consider your first effort focusing on consolidating a process for easy maintenance, and bells and whistles later. Don't use up all your yearly budget agonizing on graphic design.