The nature of all creation is sound vibrations. “And God said let there be light” in Genesis. Thus the smallest units of our own body-mind-spirit are sound vibrations. When we chant mantras (which are scientifically designed patterns of vibrations by great sages who knew their effects,) we attune our whole being to the divine vibrations. Different mantras assist us to remove our accumulated karma in different ways.
The highest, most effective mantra is the Gayatri mantra, particularly the long version: Om Bhu Om Bhuvaha Om Swaha Om Maha Om Janaha Om Tapaha Om Satyam Om Tat Savitur Varenyam Bhargo Devasya Dhi’mahi Dhiyo Yona’ha Prachoda’yat. This is the mantra recommended to all, whether Vishnu or Shiva or Devi worshippers. Children are initiated into it at 8 years old, the age that the ancient sages determined as being mature enough to be responsible for one’s own acts, karma. It is recommended to chant it first thing in the mornings, predawn and also at dusk, if possible. It is the only mantra to take the vibrations through the brain, keeping it healthy.
In chanting this mantra, one spiritualizes every phrase by beginning with Om. Each of the Seven Luminous Lokas are named, starting with Bhu/Earth, and simultaneously one should visualize taking our own energies (both prana and kundalini) through each chakra, including the 7th chakra, just above the head. The rest of the mantra takes us through our sun (Savitur) to Devasya, the dwelling place of the Devas/Devis (the Shining Ones,) then making our request to them to enlighten us: body, mind and spirit.
The Maha Mantra is correctly Rama first, then the line for Krishna, following their chronological appearances in the Earth plane. This is the mantra considered to be best for regular use in this Dark Age: Hare Rama Hare Rama Rama Rama Hare Hare; Hare Krishna Hare Krishna Krishna Krishna Hare Hare.
For healing, all Rama mantras are the best. Just chanting Rama Rama Rama . . . repeatedly will balance the currents (Ida and Pingala) in the body. Om Sri Rama Jai Rama Jaya Jaya Rama is called the Taraka Mantra, because like the Devi Tara, it takes you across the Ocean of Samsaras. This means it sands away a bit of your karma with every repetition.
The Maha Mrityunjaya mantra of Shiva defeats death and avoids accidents. It is often chanted by and for people with serious diseases. We also chant it before driving/riding in a car. It is Om Tray’ambakam Yaja Mahae Sugan’dhim Pushti Varda’nam Uvaru’kamiva Bhanda’nan Mrityor Muksheeya Mamri’tat.
There are many others for different purposes/attraction of certain energies. Lakshmi for abundance of all kinds, Saraswati for true knowledge, the arts, spiritual discipline, and Durga for protection from negativity, inner and outer. There are many Ganesha mantras for various purposes both esoteric and mundane.
All mantras ameliorate our karma. Chanting aloud is best for something you desire to manifest on Earth, including healing. Chanting silently is the most effective otherwise, because it is at the highest vibration.
[Sanskrit is pronounced with the emphasis on the first syllable, unlike English.]