This wiki article gives an overview of the Samudra Manthana.
What was the very first thing/person that came out of it?
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The story of Samudra Mathana is described in several Puranas and both of the Itihasas.
In Srimad Bhagavatam, the Eighth Canto details the story of Samudra Mathana from Chapters 5 to 11.
In the Seventh Chapter, this is said:
SB 8.7.18 — The fish, sharks, tortoises and snakes were most agitated and perturbed. The entire ocean became turbulent, and even the large aquatic animals like whales, water elephants, crocodiles and timiṅgila fish [large whales that can swallow small whales] came to the surface. While the ocean was being churned in this way, it first produced a fiercely dangerous poison called hālahala.
In Srimad Ramayana, the Samudra Mathana is related by Vishvamitra to Rama and Lakshmana in the 45th Sarga of Balakanda. In that, he says this:
"After a thousand years, the Thousand-headed serpent Vaasuki, which is being used as churning rope, is incapacitated to bear the friction of churning and fanged the cliffs of Mt. Mandara. Thereby a great lot of venom is disgorged from the heads of that serpent Vaasuki, which venom on melting the rocks of Mt. Mandara became the holocaustic poison called haalahala." (1.45.19)
In the Mahabharata, this is described in the Astika Parva of the Adi Parva, in the 19th Chapter.
In the Mahabharata however, Chandra is said to appear first and the Halahala Poison seems to appear last.
"Ati Nirmathanad Eva Kalakutah Tatah Parah|
Jagadaavrtya Sahasa Sadhoomo Agniriva Jvalan|| (1.19.42)
"Because of great churning, there appeared then the deadly poison, which enveloped the world with its vapours, resembling fire, which burns everything."
This is described after describing the various ratnas that emerge from the ocean, beginning with Chandra and ending with Airavata. But after describing the swallowing of the poison by Mahadeva, Sauti once again describes the asuras desiring to possess Lakshmi and Amrita, even though they have already emerged.
This difference can be reconciled in three ways:
By the third method, we can assume that the poison was the first to appear. The verse reads, "Kalakutah Tatah Parah" which can mean, "the deadly poison, then (emerged)."
Or it can also read, "the deadly poison, after which (Tatah Parah), (everything else emerged)."
This is similar to how Shukabrahma Rishi says that he learnt Bhagavatam at the beginning of Dvapara Yuga when he actually learnt it at the end. The analogy made is that when we consider a tree, the roots of the tree are its beginning, but we call its leaves and branches as the beginning as that is what we first notice. Similarly, Shukabrahma Rishi calls the end of Dvapara as the beginning.
In this case too, although the roots of the tree - Kalakuta poison - is the first, the leaves of the tree - Chandra, Lakshmi, Apsaras and others - are described first, and the poison is described last.
Therefore, we can conclude that by (most) scriptural accounts, the Kalakuta poison was the first to emerge during Samudra Mathana.