As someone who has a basic understanding of Java(purely on the client side, haven't done anything with NodeJS), should I continue with refining my knowledge in ES5, or just jump straight into ES6? This site looks really neat, I should add.
Java != JavaScript. While offering some cool new things, ES6 is overall a fairly incremental change. I would concern myself with learning the fundamentals of the language first.
You will need to use Babel or another processor for the newer syntax and features, which will compile you ES5ish JavaScript that browsers will mostly understand.
Compiling JavaScript is one solution to the problem that you have no control over the client interpreter and the 'version' of your code that it supports. It isn't an ideal solution, but it means we can move the language forward without worrying about breaking everything.
Edit: The Unicode in strings one teaches you both the \uXXXX and \u{xxxxxx} syntaxes, yet the former isn't new.