If what you are after is to expand your knowledge of website design, I would suggest hosting your site on Github. Github offers a services called Github Pages in which you can host your site for free. You are offered one site for your account, and then you have unlimited project sites. I have used the site to host and test websites myself, it is very simple and offers an easy way to test your websites on a mobile platform, which is perfect for supporting your learning of responsive design especially. https://pages.github.com/
Edit: lots of edits to change wording and markup
Maybe try SauceLabs - I have no personal experience with it but I believe it's closer to how Litmus works than BrowserStack.
(fwiw, I personally prefer BrowserStack to litmus because just looking at screenshots doesn't help me much when building interactive sites -- but I can understand that different testing styles are a better fit for different situations, so I don't think there's "one true best" way).