Thanks for all the great responses guys!
Still going to stay away from Unity, as I feel that I don't nearly have enough experience to go into that.
This tutorial is a good starting point. It's easy and short, and gives you some insight in how games are supposed to work (game loop, update and render logic, handle user input...) and also serves as introduction to canvas API, which I recommend to learn if you want to make games with JavaScript.
After that, you can spend some time trying to make simple games (as Snake, Pong, Breakout...) and learning deeply the canvas API.
I'm going to start there and then invoke the power of Google to learn more about canvas API. Thanks for the link Avalander!
You're welcome. It's not always easy to find good tutorials, so I'm glad I helped.