in order to minimise facial distortions (subject distance should generally be about 2-3m) while ensuring sharp eyes and a beautifully defocussed background, the classic lens for high quality portraiture is usually one with a focal length in 35mm terms of 70-120mm and a wide aperture, at least f/2.8 but in some cases, even down to f/1.2, although such lenses are big, expensive and more difficult to focus even with AF.
the requirement for a wide aperture usually means most zoom lenses are not as good although a 70-200mm f/2.8 is popular.
the requirement for shallow depth of field usually means a small sensor such as in point and shoot cameras is not as good, while a full frame 35mm or even medium format is closer to the generally accepted goal.
a wide angle lens usually requires one to get closer to the subject which not only can be intimidating but exaggerates and distorts relative size of facial features, making closer objects such as the nose bigger. Wide angles can be used and are often used in more creative, artistic portraits for impact where a faithful representation of the face is not required.
a longer telephoto requires more distance from the subject but can result in flatter facial features and a loss of intimacy as well as potentially sharpness and contrast. Glamour photographers often use these in outdoor shoots to compress the background and remove distracting features or emphasise a distant background feature.
if the subject image size is kept constant by moving in or away from a subject, then the degree of background blurriness is mainly dependent on the f/ratio and NOT on the focal length.
the aesthetics of the defocussed background (bokeh) is usually best with lenses with circular iris diaphragms so the more blades, the better as a general rule.
an internally focusing lens (IF) is an advantage as the front element does not keep moving in and out, distracting the subject.
wedding photographers often need a wider angle lens such as a 50mm f/1.2 for full length shots in addition to the usual portrait lens and perhaps a 24-70mm zoom for group shots and a 70-200mm zoom for close ups at a distance.
for an action portrait shoot such as indoor sports, toddlers crawling or animals, then a fast and accurate AF mechanism becomes critical.
for street photography, the requirements are usually different as you wish to get the subject in context with their environment and this is usually best achieved with a mild wide angle such as a 35-50mm in 35mm camera terms.
for social parties where group portraits in confined spaces are the priority, a lens with focal length 40-60mm in 35mm terms may be required.