The simple reason why Orthodox priests wear beards is because, as a Nazarene, Our Lord had a beard, as can be seen from any icon. Since the priest is a dispenser of sacramental grace and an icon of Christ, he should physically resemble Our Lord, not only in wearing a robe or cassock (which need not at all be black, contrary to popular myth), but also in being bearded and having the same hairstyle (long hair with a parting down the middle). Sometimes this is not possible, especially if the priest has to do a secular job (and also if the priest's wife objects to long hair and untrimmed beard!) However, I have not answered the somewhat more complex second part of your question.

In the Roman Empire it was the custom for men to shave. Not to shave was to be a 'barbarian', i.e. not be a Roman and therefore be culturally inferior. This custom of shaving was particularly strong in the Western part of the Roman Empire, where Rome was. Even in the Eastern part of the Empire beardless priests were still common up until the fifth century. Here, however, the sense of the physical appearance of Christ and the need for clergy to resemble Him dominated and in the East beardless clergy had disappeared by the eighth century at latest.

In the West hermits and monastics also had long hair and beards, like St Martin of Tours. However, the parish clergy came to a kind of compromise. Although in order to avoid seeming effeminate, Western Orthodox clergy did not shave, they nevertheless trimmed their beards quite closely. This is clear from icons of St Leo the Great or St Gregory the Great. Unfortunately, this tradition of trimmed beards was lost with the tyranny of Charlemagne at the end of the eighth century. With his massive 'barbarian' inferiority complex, it was his desire in all things to imitate pagan classical Rome. It was therefore under him that Western clergy were ordered to shave regularly. For example at the Council of Aachen (816), it was stipulated that priests and monks were to shave every two weeks.

Despite this, until the beginning of the eleventh century most hermits and bishops too were still bearded. Nevertheless, by the end of the eleventh century most priests and monks shaved regularly, at least ten times a year, if not much more frequently. In particular, in 1080 Hildebrand, Pope Gregory VII, tried to enforce shaving. All this was in pure imitation of the practices of pagan Rome. In the sixteenth century beardlessness for Roman Catholic clergy was enforced by further canons, which appear to have been dropped since the Second Vatican Council. (For the best and perhaps definitive survey of this question, see 'Apologia de Barbis' by Burchard of Bellevaux edited by R. Huygens with an introduction on 'Beards in the Middle Ages' by Giles Constable, Brepols, 1983).

The third part of your question concerns tonsuring. Perhaps you do not realise it, but all Orthodox monks are tonsured (as are all Orthodox, at baptism and chrismation). Today, their tonsure, however, is symbolic. Until the fifteenth century, it most certainly was not and consisted of a round tonsure on the crown of the head exactly like the ancient but not late mediæval Western one. A glance at any icon of St Gregory Palamas will confirm this halo-like tonsure. Under the influence of hermits this actual tonsuring fell out and long hair came in. With monastic influence, the custom of long hair even for married clergy has become the norm (though St Paul would not have approved: 'Doth not nature itself teach you, that, if a man have long hair, it is a shame unto him?' 1 Cor. 11, 14 ).

In conclusion it can thus be said that the wearing of beard and long hair by Orthodox clergy, wherever it is possible, has come from the desire to physically resemble Christ. It is to be hoped that this physical resemblance is but a symbol of the spiritual resemblance of Christ's humility, which is the aim of our life.