"What are the different types of macro lenses"?

There are "Macro" lenses and there are Macro lenses. As others have mentioned, a true Macro lens will magnify the subject to a 1:1 ratio which is generally a desirable feature. Many lenses will be marketed as 'Macro' lenses even though they don't magnify down to 1:1 so be careful to check the actual magnification factor of the lens you're interested in purchasing.

"What are the different advantages?"

Two important factors when considering a macro lens are the magnification factor and the aperture range. Lenses with a higher magnification ratio, 1:1 or even 5:1 are useful for small or detailed subjects and lenses that have apertures down to f45 or f64 can create a larger depth of field. As a side note, the ability to magnify down to 1:1 isn't necessarily critical for all macro work and if you're open to slightly lower magnification, 1:2 say, you can use Tilt-Shift lenses or Zeiss optics that open up to f2.0. Or, since 1:1 macro lenses tend to be primes, you can use one of many zoom 'Macro' lenses that have lower magnification.

"What is recommended for the best rendition?"

Well thats a tough question that depends on what kind of work you plan on doing. If you plan on photographing insects or anything that might fly off or bite you, you'll want a larger working distance from the subject so you'll want to look at the 150-180mm range of macro lenses, or even using a 300mm lens. The downside to a longer focal length is camera shake and vibration will be more of a problem which can drive you towards the 50-65mm range of lenses. Of course the problem there is not only are you so close to your subject you could scare it, but you can block the light with your camera. I personally feel that the 90-105mm area is the best compromise of working distance and vibration/camera shake, plus in that area there are several lenses that offer image stabilization for shooting hand-held.