Javascript Method Naming lowercase vs uppercase

It honestly depends. Your first method is called Camel Coding, and is a standard used by Java and C++ languages, and taught a lot in CS.

The second is used by .NET for their classes and then the _camelCode notation used for private members.

I like the second, but that's my taste, which is what I think this depends on.

A popular convention in Javascript is to only capitalize constructors (also often mistakenly called "classes").

function Person(name) {
  this.name = name;
}
var person = new Person('John');

This convention is so popular that Crockford even included it in its JSLint under an optional — "Require Initial Caps for constructors" : )

Anything that's not a constructor usually starts with lowercase and is camelCased. This style is somewhat native to Javascript; ECMAScript, for example (ECMA-262, 3rd and 5th editions) — which JavaScript and other implementations conform to — follows exactly this convention, naming built-in methods in camelcase — Date.prototype.getFullYear, Object.prototype.hasOwnProperty, String.prototype.charCodeAt, etc.