Since you're just getting started as a web developer I think the suggestion to try out GitHub Pages, Jekyll, and setting up your own domain name and perhaps even hosting your own site on your own hand-built platform would really teach you what you need to know to do your job well. Even if all of those parts of the job won't be what you do day-to-day just knowing what is involved can help you communicate with any team you may work with in the future.
As an aside, I run a hosted-CMS called Barley that allows you to use just use HTML, CSS, and JS to run and host your site. It would not teach you as much about your new career as it would if you use your own host, your own platform, etc. but it might be something fun to poke at. It comes with a 30 day free trial and includes unlimited storage, content edits, dropbox syncing, and more but since you're just starting out if you'd like 1 personal site for free for life send me an email http://plainmade.com/company -- Barley is here: http://getbarley.com