XML and JSON are just data formats, they are neither slow or fast.
Also JavaScript running in a web browser does not have the abililty to direclty connect to a MySql database.
Here is a high level overview of what needs to happen in order to do what you are asking:
-Write javascript that talks to a web service.
-The web service will query the database for the information you want (in your case the postal code that coresponds to the lat/long you provide).
-The web service will take the data from the database and format it as XML or JSON, and the webservice will return that to the browser, where your javascript will pick it up, parse it, display it, or do whatever you need to do with it.
Also, since the webservice can't be hosted on your site (BC doesn't have any way to do that), it will have to be on another domain and hosted seperately from your primary site. Something like webservice.example.com instead of www.example.com. However because of this, the browsers built-in security system will take over, and not allow the data from the external service to be consumed. To get around this limitation you will need to configure your webserivce to send data as JSONP, or use CORS, which is unfortunately not supported in some older browsers.
There are lots of differently ways to create and host a webservice.
However, I'd first look for a pre-built service that does what you want.
