It is very difficult to say whether Sri Ramakrishna chose Maa Kali or Maa Kali chose Ramakrishna to express Her divinity through him! It looks to me that the later was more true.
Worshiping Lord Raghuvir (Ram) and Sitala Devi (A form of Durga) as family deities was in vogue in Sri Ramakrishna’s family. But there doesn’t seem to be any specific instance of Sri Ramakrishna’s ‘attachment’ to Sitala Devi for worship in his early years.
Sri Ramakrishna’s first “encounter” with Maa Kali seems have happened when he took a pilgrimage as a boy along with local women to Anoor Visalakshi Temple. As he was walking with the women singing bhajans on Divine mother, he suddenly went into a trance – attaining bhava Samadhi and getting immersed in overwhelming emotions on Devi.
Later, in his late teens, he went to Kolkata to assist his elder brother Ramkumar, who was earning the very livelihood through practicing purohitam (priesthood) for the family stricken with poverty at Kamarpukur. Ramkumar got appointed to to Dakshineswar Kali temple as the priest and Sri Ramakrishna too shifted to the temple premises only very reluctantly. Interestingly, the orthodox Brahmin mindset he had in those days made him decline to eat Kali’s Prasad!
I believe it was gradually afterword that Dakshineswar Bhavatarini Kali started Her divine play of ‘possessing’ the reluctant Village Brahmin teenager and making him her own and finally making his Self her own divine abode!
The rest is history.
Kali worship, Tantra and Sri Ramakrishna
Regarding significance of Kali Worship, Shaktas will give lots of reasons based on Puranas and Tantra Shastras about the superiority of Kali worship over other sects. In my opinion, it was another very strong sect, (like Gaudiya Vaishnavism in Bengal) existing in those periods, thanks to the widespread practice of Tantra amid Bengalis.
It may be pointed out that Sri Ramakrishna practiced Tantra under the methodical and strict guidance of Bhairavi Brahmani and attained the pinnacle of divine experience as per Tantra Shastras. But during his days, Tantra Shastra had attained quite a bad reputation because it was conveniently misunderstood and practiced by many to enjoy drinking and sex. Leaving behind the core idea of transcending those meaner pulls to attain divinity (Unity of Shiva and Shakti) through enjoying and overcoming, Tantra in practice had considerably degenerated those days.
By the strength of his divine experience, Sri Ramakrishna strongly warned against those practices of Tantra; he pointed out that the chances of falling were rather more than succeeding by the secret practicing of indulgence in the Pancha Makaras — madya (wine), māṃsa (meat), matsya (fish), mudrā (parched grain) and maithuna (sexual intercourse) of the Tantra.
Sri Ramakrishna prescribed Bhakti as the best means for woshipping divine mother Kali. For him, Maa Kali and what Upanishads call Brahman are one; Maa Kali is Brahman and Maya rolled into one and inseparable.
In the path of Bhakti on Kali, again, Sri Ramakrishna recommended a relationship of a child with its mother (Santhana bhava) as the best and detested a relationship as a lover (Madhura bhava).
We should not make the mistake of compartmentalizing Sri Ramakrishna to be a Shakta. He was a vaishnava amidst Vaishnu Bhakts; he was a Shaivite amidst Shiv Bhakts. He was an Advaiti amidst Jnanis. He was a yogi amidst Raja yogis.
We must also remember this: Sri Ramakrishna, when he practiced Nirvikalpa Samadhi under the guidance of Tota Puri had to mentally severe his emotional dvaita relationship with Maa Kali; as per Tota Puri’s instruction, he had to cut and get rid of Kali’s form from his mind (by using the sword of jyana) before he experienced Nirvikalpa Samadhi where the experience of God is beyond name and form.
However, for the sake of ‘coming back’ and teaching the world his all-encompassing divine knowledge, Maa Kali instructed him to remain in Bhava Samadhi (in a state where he could be in communion with God with name and form only).