Responsive Web Design (RWD) is a design approach to render your web sites to easily to different devices size like mobile phones and tablets. My preferred RWD is jQuery mobile framework. It is simple to setup and allows you to create RWD quickly. Have you test drive RWD before?
There are a few RWD format. The most popular frameworks are jQuery and Bootstrap. My personal preference is jQuery mobile because I can set it up easily and it is easy to configure for different UI (User Interface). Do take some time to review and test with different type of framework. I recommend that you use the popular framework because there will be more sample codes and active community. It is best to set some use cases and selection criteria for your testing.
RWD is a basic norm for web sites design framework across different devices. This reduce your efforts to code differently for laptop and mobile. In addition, RWD framework is easier to setup and deploy. There is no reason not to utilise RWD for your website.