Welcome to the forum, there's a wealth of knowledge here for the asking.
Congratulations on your new NEX-6. It's also my newest camera and it surprisingly capable for such a small camera.
The distortion you mention is quite nasty from 16 to about 35mm. The in camera correction works quite well. I've noticed that the in camera processing crops the edges quite a bit. I process with Aperture which does not even offer any kind of lens correction so I just have to deal with the distortions for now if I choose to shoot raw.
The biggest problem I have with shooting jpegs to get the corrections is the lack of room that I have to work with. When shooting raw there seems to be a lot more room to work with in regards to pulling down the highlights and pulling up the shadows. I notice in Aperture at least, that the images seem to have a flat washed out look if I process the jpegs the same way I do raw files.
I also use Elements for some effects that require using layers but I never do my basic processing with it.
You may not be as happy with the lens correction in Lightroom as compared to the in camera corrections but I would gladly take any kind of lens correction compared to none like I have now if I choose to shoot raw.
Talknex.com has a lot of information available.