Universal seed mantras: The foundational, primary sounds are called seed or bija vibrations in Sanskrit. Such universal sounds can also be called basal, prime, primordial, essential or basic sound vibrations, as well as other descriptive names.
Om is such a sound, especially when focusing on the Mmmmm... sound vibration, which is somewhat like mentally remembering the sound of a buzzing bee. Both inhalation and inhalation might be done smoothly and slowly, while remembering that Mmmm... sound mentally. Om Mantra can be used as a seed vibration alone, or along with deeper meanings.
Soham is a universal mantra vibration, with Sooo... being remembered with inhalation and Hummm... being remembered with exhalation.
Ahhh... can be remembered with inhalation and Ummmm... remembered with exhalation.
Many other such sound vibrations can also be used, whether or not coordinated with breath. For example, any of the single-syllable vowel sounds can be used, with or without an Mmmm... sound at the end.
It is the practice itself that will convince one of the viability of such universal sound vibrations as means of relieving the autonomic nervous system, while calming and focusing the mind. Mantra practice like this will prepare the mind for deeper meditation beyond the syllables of the mantras.
Longer mantras: There are many longer mantras in many languages. Some are like positive affirmations and some are for specific, desired benefits. Some are related to religions, and some are not. The principles of using mantra that are listed below are universal, applying to all of the many types of mantras.
Compact prayer: Some mantras can be described is as short, compact prayers. One can easily think of examples where a particular sentence or phrase from a longer prayer or writing forms a compact prayer or mantra. Once again, the principles below are universal, applying to any of these types of mantra.