How you make a website is up to you.
Back in the day, web design was easy. Everyone's computer monitor was exactly the same width and height. Almost everyone used the same browser. Today, things are more complex. You are losing business if your web site doesn't work on everything from an iPhone to a big screen TV. In addition, today's browsers render web pages differently... in some cases substantially differently.
To cope with these challenges, you have three choices:
Purchase an off the shelf template
A variety of companies have produced customizable responsive templates. On the plus side, they're less expensive than building a site from scratch. In addition, ongoing support is provided by the company. Also, a template which is popular has already been tested and debugged and has a good chance to work reliably. On the negative side, they look just like everyone else's.
Make a custom site from scratch
To get the look you want, you may choose to have your website made from scratch. This option, of course, provides almost endless flexibility limited only by what modern web browsers can do. This is also likely to be an expensive option consuming endless hours of a web developer's time. More concerning than that is the question of ongoing support which is expensive and generally tied to the developer who created it. This option is appealing for businesses large enough to afford an IT department but it may be inappropriate for smaller businesses.
Use a suitable design tool
Often a balance can be found between a cookie-cutter design and a custom-built model. Starting with a content management system (such as Joomla) and using proper design tools (such as Artisteer), I can create a custom website with the look and usability you envision at much less than the cost of a site created from scratch. These tools are well tested. In addition, as technology changes, updating your site requires very little effort and is simple to do. You remain in control of your website, from the look and feel to content manipulation.
In the end, a choice must be made between design flexibility and cost. Choosing wisely is critical for the long-term success of your web site. I can discuss these options with you so you understand the pros and cons of each and choose the one that is best for you.