What's the best way to go about making board games such as Chess, suitable for playing in a browser, and why?

I have a board game idea (imagine a game such as chess, or scrabble) which I want running in a browser, and I just started working with HTML, CSS, JS, and a bit of jQuery. It's just a small project I want to do for practice. I envision making it possible for multiplayer functionality over the internet in future. With my current knowledge, I think the aforementioned languages are sufficient for making my game. If I wanted to make it playable on a mobile device with a large screen such as a tablet, what should I use to make it compatible? What of devices with smaller screens such as mobile phones? (pinch and expand maybe?) However I am inexperienced and unsure, and want to use App Engine to deploy the website with the game. Is this the best way to go about this, or there are better tools to use? I am relatively new to programming and have dabbled with C++ and Java before, so if there are better tools out there to use, please suggest those which are simple enough to beginners like me. Thanks in advance.