Wordpress is a good choice if you want a CMS (Content Management System). You can add themes that are responsive, plus the twenty-fourteen theme is already responsive.
You stated you wanted to brush up on web design skills, and Wordpress is a complete solution, so I'm not sure it's what you want. If you're wanting to build websites from scratch, but you want a good starting point, try either [Bootstrap 3 or [URL="http://foundation.zurb.com/"]Foundation 5](http://getbootstrap.com/). Both are great starting points for building modern responsive websites.