The differences between the two mantras are subtle, and have already been covered in depth on our forum in this discussion. To understand this explanation, you will need to be familiar with Krsna's pastimes as described in Krsna Book and the classification of rasas or transcendental relationships with God as presented in Nectar of Devotion.

The Vedas are eternal, therefore they contain instructions for self-realization in all times, places and conditions. The Lord also appears Himself in every yuga to give the yuga-dharma, or process of self-realization for the age. The yoga system of silent meditation was recommended in the Satya-yuga, the Golden Age , several million years ago. The actual meditation practice was to always meditate on Viṣṇu. In the Tretā-yuga one could practice yoga by performing great Vedic sacrifices, and in the next age, Dvāpara-yuga, one could achieve perfection by temple worship.

Generally we recommend that students go through Sri Isopanisad, Secrets of the Soul, Bhagavad-gita and then the principal work of the Esoteric Teaching, Srimad-Bhagavatam. You can also read my introductory book, Search for the Absolute Truth.

The transcendental vibrations of the mantra increase the flow of life energy, resulting in better circulation and vitality. Actually transcendental sound vibration is the nourishment the soul craves, because it confirms our transcendental nature and spiritual identity. Remember, the quality of our consciousness is determined by the quality of the impressions we take in. A life without spiritual impressions would be dreary indeed, like poison for the soul.

Actually it is very simple to chant the Holy Name of the Lord.

You should begin by chanting on a string of 108 wooden beads similar to a rosary. Chant one mantra on each bead until you reach the head bead, then turn around and go the other way.

The answer is given by Lord Caitanya:

"Lord Caitanya recommended, kīrtanīyaḥ sadā hariḥ: [Cc. adi 17.31] one should always chant the holy name of the Supreme Lord, Kṛṣṇa, because Kṛṣṇa is the most suitable name of the Supreme Personality of Godhead. The name Kṛṣṇa and the Supreme Person Kṛṣṇa are nondifferent. Therefore, if one concentrates his mind on hearing and chanting Hare Kṛṣṇa, the same result is achieved." [Srimad-Bhagavatam 3.28.9 Purport]