This chapter of the Anushasana Parva of the Mahabharata says that Shaunaka was a descendant of Vitahavya, a Haihaya king who got magically changed into a Brahmana by the sage Bhrigu:
Vitahavya had a son named Gritsamada who in beauty of person was a second Indra. Once on a time the Daityas afflicted him much, believing him to be none else than Indra. With regard to that high-souled Rishi, one foremost of Srutis in the Richs goes like this viz., He with whom Gritsamada stays, O Brahmana, is held in high respect by all Brahmanas. Endued with great intelligence, Gritsamada become a regenerate Rishi in the observance of Brahmacharyya. Gritsamada had a regenerate son of the name of Sutejas. Sutejas had a son of the name of Varchas, and the son of Varchas was known by the name of Vihavya. Vihavya had a son of his loins who was named Vitatya and Vitatya had a son of name Satya. Satya had a son of name Santa. Santa had a son, viz., the Rishi Sravas. Sravas begot a son named Tama. Tama begot a son named Prakasa, who was a very superior Brahmana. Prakasa had a son named Vagindra who was the foremost of all silent reciters of sacred Mantras. Vagindra begot a son named Pramati who was a complete master of all the Vedas and their branches. Pramati begot upon the Apsara Ghritachi a son who was named Ruru. Ruru begot a son upon his spouse Pramadvara. That son was the regenerate Rishi Sunaka. Sunaka begot a son who is named Saunaka.
This chapter of the Bhagavatam gives a different ancestry, starting from the lunar dynasty king Pururavas:
From Purūravā came a son named Āyu, whose very powerful sons were Nahuṣa, Kṣatravṛddha, Rajī, Rābha and Anenā. O Mahārāja Parīkṣit, now hear about the dynasty of Kṣatravṛddha. Kṣatravṛddha’s son was Suhotra, who had three sons, named Kāśya, Kuśa and Gṛtsamada. From Gṛtsamada came Śunaka, and from him came Śaunaka, the great saint, the best of those conversant with the Ṛg Veda.
But despite the discrepancies, they're clearly the same person, because both Gritsamada and Shunaka appear as ancestors. It may be a case of interpolation or Kalpa Bheda.
In any case, Shaunaka's Guru Parampara is described in this chapter of the Vishnu Purana:
I will now give you an account of the Sanhitás of the Atharva-veda. The illustrious Muni Sumantu taught this Veda to his pupil Kabandha, who made it twofold, and communicated the two portions to Devaderśa and to Pathya. The disciples of Devaderśa were Maudga, Brahmabali, Śaulkáyani, and Pippaláda. Pathya had three pupils, Jájali, Kumudádi, and Śaunaka; and by all these were separate branches instituted. Śaunaka having divided his Sanhitá into two, gave one to Babhru, and the other to Saindhaváyana; and from them sprang two schools, the Saindhavas and Munjakeśas.
Also, a story involving Shaunaka is described in this chapter of the Chandogya Upanishad:
Once while Saunaka Kâpeya and Abhipratârin Kâkshaseni were being waited on at their meal, a religious student begged of them. They gave him nothing.
He said: 'One god--who is he?--swallowed the four great ones 3, he, the guardian of the world. O Kâpeya, mortals see him not, O Abhipratârin, though he dwells in many places. He to whom this food belongs, to him it has not been given.' Saunaka Kâpeya, pondering on that speech, went to the student and said: 'He is the self of the Devas, the creator of all beings, with golden tusks, the eater, not without intelligence. His greatness is said to be great indeed, because, without being eaten, he eats even what is not food. Thus do we, O Brahmakârin, meditate on that Being.' Then he said: 'give him food.' They gave him food. Now these five (the eater Vâyu (air), and his food, Agni (fire), Âditya (sun), Kandramas (moon), Ap (water)) and the other five (the eater Prâna (breath), and his food, speech, sight, hearing, mind) make ten, and that is the Krita (the highest) cast (representing the ten, the eaters and the food). Therefore in all quarters those ten are food (and) Krita (the highest cast). These are again the Virâg (of ten syllables) which eats the food. Through this all this becomes seen. He who knows this sees all this and becomes an eater of food, yea, he becomes an eater of food.
This story, by the way, is part of a Brahmavidya called the Samvarga Vidya, which I discuss here.