The real question is this:
I am trying to figure out the effect of font smoothing in my web page. On my LCD panel the text looks the same with font smoothing on/off.
Are there are any particular fonts that need smoothing. Can you suggest any example font best suited for font-smoothing (i.e. it gives good result on applying smoothing).
By default most modern web browsers are going to use font smoothing. You can turn it off though to see how it will look on people that are not using it. For example here is an article on doing so in IE7.
In theory all fonts should benefit, but in pratice how much they benefit depends both on the font used and the font rasterization technique used.
A couple of good articles on font rasterization are How Sub-Pixel Font Rendering Works and Text Rasterization Exposures