1. Mahamrityunjay Mantra: This is the best Mantra for health without any doubt. Everyone must chant 1 rosary daily in order to be healthy and disease free and stay away from chances of Akal Mrityu. One must very well understand that just chanting the Mantra is not enough. If on one side you are chanting this Mantra and on the other hand eating unhygienic foods like Vadapav, Dosa, Chinese foods,etc. Even god won't save you from the diseases because you yourself don't want to stay healthy.
2. Hanuman Chalisa: It is very necessary to chant this Stotra 11 times daily in order to live a peaceful life and start away from negative effects of Shani Dev. Other than that, it is very powerful for removing Vipreet Baadha.
3. Durga Mantra: Om Hreem Dum Durgaayey Namah. The Mantra is one of the dearest Mantras of Durga and it grants everything from wealth, name and fame to removal of enemies. The person who takes a Sankalp and does this Japa 1 lac times, Maa Durga herself grants him Asht Siddhis.
For daily Japa, This Mantra should be chanted for 3 rosaries using a Rudraksh Mala. During Japa, one must wear one Rudraksh rosary and do Japa with another rosary.
4. Hare Rama Hare Krishna Mantra: this Mantra is without any doubt the ultimate Mantra for getting Moksha. Remember, the person who doesn't worship Rama or Krishna is bound to suffer. As a true Sanatana Dharma, their worship is unavoidable and necessary. This Mahamantra should be chanted for 21 rosaries daily without fail. One achieves Moksha when he completes 3 crore 50 lac chants.
5. Shivling Puja: every Monday , one must do Shivling Puja in order to get prosperity and success in life. One must offer Chandan Paste, rice, black sesame, honey and Bel Leaves every Monday and chant 1-5 rosary of ॐ नमः शिवाय in the Shivalay itself.
6. Shree Sukt and Lakshmi Sukt: these Stotras are best for people who want to get extremely rich. These Stotras should chanted 11-11 times daily during dusk time.
7. Ganesh Dwadash Naam Stotra: this Stotra is very very powerful and it's energy can be felt from the first recitation itself. The Stotra fulfills all kinds of wishes and keeps away all kinds of obstacles. It gives everything-wealth,health,son,,wish fulfillment.
8. Gayatri Mantra: this Mantra should be chanted for 1 rosary at dusk daily. Reciting the Gayatri Mantra during dusk is a rule in Sanatana Dharma.
9. ।। ॐ नमो भगवते रुद्रावताराय सर्वरोगहराय सर्वशत्रुसंहारणाय सर्ववशीकरणाय रामदूताय स्वाहा ।।
This Mantra is Amogh and it destroys all enemies, and attracts everyone in the world.
The person who recites these very useful 9 Golden Mantras without any doubt get all round success in life.
Again keep in mind that faith is everything and mere chanting not going to help. If one doesn't have love and faith in God, mantra will never ever work for him.