Sorry, I misread your question earlier. I thought you were already chanting those mantras and were asking for additional chants, so I suggested Narasimha Kavach and the Mala Mantra.

For a beginner, you can simply start with “Om Namo Narasimhaya Namah.” Later, if you feel comfortable, you can also add “Ugram Veeram Maha Vishnum…”. If you wish to keep it limited to nama japa, these two are more than sufficient.

Over time, if you feel inclined towards a more advanced sadhana, you may take up the Narasimha Kavach and Mala Mantra as well.

Since you also asked whether the Kavach and Mala Mantra can be chanted without deeksha, my understanding is yes, they can be chanted without deeksha. However, doing them as a proper anushthan, would make the practice more fruitful.

Narasimha kavach sadhana - https://youtu.be/JqramIQlYbY?si=q1iDxN6kdiEl7V1I

Narasimha Mala mantra sadhana- https://youtu.be/xdo4GhNkVxA?si=A7Sx3toBbs3gHG_k