PLEASE NOTE: I come from an irreligious/atheist family. We do not have any Ishta-DevatA or Kula-DevatA.
Like most people from irreligious families, I am significantly ignorant of dharma. Would NAma-japa of any DevatA be beneficial for someone like me, who barely knows anything about our faith?
Also, could you give any tips for increasing devotion?
Yes, japa of a mantra obtained from a Guru is extremely beneficial.
Repeat It and Contemplate Upon Its Meaning.
Patanjali's Yoga Sutra I.28
It stands for OM in the Yoga Sutra.
Sri Ramakrishna stood up. Referring to japa, he said to a devotee: "Japa means silently repeating God's name in solitude. When you chant His name with single-minded devotion you can see God's form and realize Him. Suppose there is a piece of timber sunk in the water of the Ganges and fastened with a chain to the bank. You proceed link by link, holding to the chain, and you dive into the water and follow the chain. Finally you are able to reach the timber. In the same way, by repeating God's name you become absorbed in Him and finally realize Him."
The Gospel of Sri Ramakrishna, The Master and Dr. Sarkar, October 24, 1885
Two issues of importance have been mentioned in the comment. The questioner feels that he has no Adhikara to chant a mantra because he is not a Brahmin. I am posting below Swami Vivekananda's opinion of such a doctrine. The questioner can safely ignore the doctrine of adhikarivada.
In one of his question classes the talk drifted on to the Adhikârivâda, or the doctrine of special rights and privileges, and Swamiji in pointing out vehemently the evils that have resulted from it spoke to the following effect:
With all my respects for the Rishis of yore, I cannot but denounce their method in instructing the people. They always enjoined upon them to do certain things but took care never to explain to them the reason for it. This method was pernicious to the very core; and instead of enabling men to attain the end, it laid upon their shoulders a mass of meaningless nonsense. Their excuse for keeping the end hidden from view was that the people could not have understood their real meaning even if they had presented it to them, not being worthy recipients. The Adhikarivada is the outcome of pure selfishness. They knew that by this enlightenment on their special subject they would lose their superior position of instructors to the people. Hence their endeavour to support this theory. If you consider a man too weak to receive these lessons, you should try the more to teach and educate him; you should give him the advantage of more teaching, instead of less, to train up his intellect, so as to enable him to comprehend the more subtle problems. These advocates of Adhikarivada ignored the tremendous fact of the infinite possibilities of the human soul. Every man is capable of receiving knowledge if it is imparted in his own language. A teacher who cannot convince others should weep on account of his own inability to teach the people in their own language, instead of cursing them and dooming them to live in ignorance and superstition, setting up the plea that the higher knowledge is not for them. Speak out the truth boldly, without any fear that it will puzzle the weak. Men are selfish; they do not want others to come up to the same level of their knowledge, for fear of losing their own privilege and prestige over others. Their contention is that the knowledge of the highest spiritual truths will bring about confusion in the understanding of the weak-minded men, and so the Shloka goes:
"न बुद्धिभेदं जनयेदज्ञानां कर्मसङ्गिनाम् । जोषयेत्सर्वकर्माणि विद्वान्युक्तः समाचरन् ॥" (३-२६)
— "One should not unsettle the understanding of the ignorant, attached to action (by teaching them Jnâna): the wise man, himself steadily acting, should engage the ignorant in all work" (Gita, III. 26).
I cannot believe in the self-contradictory statement that light brings greater darkness. It is like losing life in the ocean of Sachchidânanda, in the ocean of Absolute Existence and Immortality. How absurd! Knowledge means freedom from the errors which ignorance leads to. Knowledge paving the way to error! Enlightenment leading to confusion! Is it possible? Men are not bold enough to speak out broad truths, for fear of losing the respect of the people. They try to make a compromise between the real, eternal truths and the nonsensical prejudices of the people, and thus set up the doctrine that Lokâchâras (customs of the people) and Deshâchâras (customs of the country) must be adhered to. No compromise! No whitewashing! No covering of corpses beneath flowers! Throw away such texts as, "तथापि लोकाचारः — Yet the customs of the people have to be followed." Nonsense! The result of this sort of compromise is that the grand truths are soon buried under heaps of rubbish, and the latter are eagerly held as real truths. Even the grand truths of the Gita, so boldly preached by Shri Krishna, received the gloss of compromise in the hands of future generations of disciples, and the result is that the grandest scripture of the world is now made to yield many things which lead men astray.
This attempt at compromise proceeds from arrant downright cowardice. Be bold! My children should be brave, above all. Not the least compromise on any account. Preach the highest truths broadcast. Do not fear losing your respect or causing unhappy friction. Rest assured that if you serve truth in spite of temptations to forsake it, you will attain a heavenly strength in the face of which men will quail to speak before you things which you do not believe to be true. People will be convinced of what you will say to them if you can strictly serve truth for fourteen years continually, without swerving from it. Thus you will confer the greatest blessing on the masses, unshackle their bondages, and uplift the whole nation.
The Complete Works of Swami Vivekananda, Volume 5, Notes from Lectures & Discourses, The Evils of Adhikarivada
The questioner wanted to know if he can chant Rama's name. Of course he can chant Rama's name. It is necessary to point out that initiation is necessary for most seekers to get the effect.
It is laid down by the Lord that there can be no moksha, liberation, without diksha, initiation; and initiation cannot be there without a Teacher.........
Kularnava Tantra, Readings by M. P. Pandit, Chapter X, Diksha (Initiation)
I am adding this to clarify my position on nama japa. Any one who is only chanting the Name is doing parts of Bhakti Yoga. He might not need to do anything if he has a done a lot of good karma in the previous life and in the present life and he surrenders completely to God.
Abandoning dependence on all Dharmas, come to Me as the only refuge. Grieve not; I will deliver you from all sins.
Gita 18.66
Most people do not have a good enough karmic history to be able to surrender completely to God. Hence most people need the help of mantra japa to make spiritual progress.
Some one will cite explicitly from vedas or Adivat Vedanta, I will provide you some words from the 'pravachane' of Shri Brahmachaitanya Gondavalekar Maharaj Gondavale,
English Translation:
All Sadhana's end at 'Nama'. This Sadhana is equivalent to a vehicle, in which you skip the scenery and noise that you might hear during your travel. It directly takes you to the God. Although it may feel that other sadhana are quick, they are temporary. 'Nama' is slow, but what you will achieve is permanent. The supreme path towards god, is "Namajapa".
There were four men, all had the same disease but were economically different. The doctor told the poorest to take the medicine along with Tulsi (Basil) . To the poor to take it in honey, to the rich in keshar (saffron) , and to the richest in Kasturi (musk) . The same way, one can take nama accordingly, "just take it", "take it with faith", "take it with maintaining the attitude", "take it with the thought, that there is no truth other than nama". All will receive its fruits.
-Taken from Pravachan of 27 Jan Titled: 'Nama, a Rajamarg towards God' with end note: 'all sadhana end in Nama'
One can read the original Marathi here. Also one can read official English Translation here.
This is a supplementary answer and not a primary answer as I do not consider myself an expert on this field.
If I understand correctly, you ask whether nama-japa can contribute positively to your life and well being, if practiced, given your atheistic background, along with strategies to increase devotion.
My answer in short, is yes it will benefit you. Now for the detailed answer: I would suggest you to read Hindu epics, which are most easily understood and do not contain any special terminologies/difficult concepts, and have stories/incidents which give you a glimpse into the Hindu way of looking at things, about Hindu ethics, spirituality, tradition. For example, if you are not from the Indian subcontinent, or maybe you are from an Indian, non-Hindu family, your way of looking at things will be radically different from the Hindu way. Let me illustrate with a few examples:
The deep respect for elders and one's parents that is present in the Indian tradition is not present in most other traditions.
The place of women is different in the Hindu society compared to the west. In India, a woman is not looked upon as an object, to be craved for lust, but she is looked as the loving mother who protects and nourishes every creature on this planet. Reference (answer by rickross has the appropriate references)
Because of this reason, you will find that traditional women in India do not have the same dress code as their western counterparts and are dressed more modestly. In India, we have female goddesses as well and they are worshipped as the divine mother. Reference: Who is mother Durga, why was she prayed by all gods including Vishnu to be reborn as Parvathi?
You should read some of these epics before starting any practice, else may face hurdles. Nama japa is a subconscious process that seeks to drive goodness and resilience deep inside your consciousness. If you don't imbibe the correct ideals before starting the process, the practice may be harmful for you. Some of the popular epics in our tradition are : Ramayana, Mahabharata, Shiva Purana, Bhagavatam, Vishnu Purana, etc.
Now, if you are not from India/well versed in the Hindi language (any Indian language for that matter, say Marathi, Gujarati, Tamil, etc.), then you may find trouble finding the correct books. Hinduism has been under constant attack from greedy evangelizing religions who take every opportunity to attack Hinduism and show it in a poor light. Hence, you will find the market filled with ill-motivated so-called Hindu books, don't fall for them. Books by Gita publications are considered the authoritative versions. You may find Mahabharata and Ramayana books published by them. Alternatively, some modern Hindu authors have written some really nice books that seeks to preserve the essence of the epics, but making slight changes to make it readable by English language readers. Example: Parva, a retelling of the classical Mahabharata, by SL Bhyrappa, Ramayana by Ramesh Menon, Siva- The Siva Purana retold, etc.
Here is a list of some good books on mantras/japa :
