There are many different types of websites and a variety of functionality that your site can have. You can mix features from several different types to meet your exact needs. And you can even start with one type of site and build onto it as your needs develop over time. Below, you can get a good idea of the spectrum.
Regardless of which type of website you need, your site should definitely be responsive (optimized for any type of screen viewing – whether smartphone, tablet, laptop, or desktop). With today’s prominence of smartphones and tablets, Google’s recent update began showing preference to responsive (mobile-friendly) websites in search results on April 21, 2015. All of the new websites I create are built with responsive responsive design. If you have a website that is not currently responsive, please shoot me a message to find out what it would take to make it responsive.