Smoothness often comes from a large lightsource (i.e. a softbox or umbrella) The first link you posted isn't what I'd call crisp fashion photography so I'm not entirely sure what you're after.

Crispness comes from the lens, and from post processing. The balance switches as you reduce the image size. Don't be swayed by sharp looking but tiny images! For images downsized or the web e.g. 600x400px you can take an out of focus 16 megapixel image and make it look tack sharp!

edit 3

Looking at the NYE photos it seems you're after high contrast high key images. I was immediately reminded of this shoot:

All you need for this is a bright source approximately dead on to the subject. The light I used was a small softbox which gives a softer look than the one in the gallery you posted. I also used a background light as the background was further away.

Here is the unedited version (note that you can get this look, or at least very close on camera by turning the contrast way up in the picture style or whatever the Nikon equivalent is!)

edit 2

Here is an image from a wedding which is at least similar subject matter to the Sardinia image. Here I have pushed the local contrast as far as I can:

It's not as good as the lighting was totally different (direct late afternoon sun, vs. diffuse sunlight from above) but I am getting warm? Here's the original for comparison:

edit

From this image: http://www.pbase.com/compuminus/image/28657593 it seems like sharpness and contrast is mostly what you're after. If so then post processing is the best way to achieve this, especially when you're downsizing images for the web. Here is an example of what you can do with sharpening:

Here's an image reduced to 600 pixels and aggressively sharpened:

Here's the same in focus 12 megapixel image with the same high quality macro lens and same complex lighting, but without sharpening:

And it fails to pop in the same way. In reality I would go halfway between the two!.

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As for fashion photography, you can't say it's more about the setup/capture, or it's more about the post processing. The truth is you need both for fashion photography. If either is not there it's very hard to make it up with the other.

One thing to bear in mind, you need a lot of space! Cramped indoor conditions give you very little control over your lights. Light bounces off the walls/floor and you get a muddy light with lots of different colours in it. What you want is a nice directional white light. A black walled studio is ideal, failing that shoots outdoors in a large enough space will suffice!