As far as vibhutis are concerned, they are very explicitly described in the Bhagavad-gita in the Vibhuti-yoga chapter. And for all these different types of incarnations, the fountainhead is the Garbhodakasayi Visnu
SB Canto 1
This form (the second manifestation of the puruṣa) is the source and indestructible seed of multifarious incarnations within the universe. From the particles and portions of this form, different living entities, like demigods, men and others, are created.
The puruṣa, after creating innumerable universes in the mahat-tattva, entered in each of them as the second puruṣa, Garbhodakaśāyī Viṣṇu. When He saw that within the universe there was only darkness and space, without a resting place, He filled half of the universe with water from His own perspiration and laid Himself down on the same water. This water is called Garbhodaka. Then from His navel the stem of the lotus flower sprouted, and on the flower petals the birth of Brahmā, or the master engineer of the universal plan, took place. Brahmā became the engineer of the universe, and the Lord Himself took charge of the maintenance of the universe as Viṣṇu. Brahmā was generated from rajo-guṇa of prakṛti, or the mode of passion in nature, and Viṣṇu became the Lord of the mode of goodness. Viṣṇu, being transcendental to all the modes, is always aloof from materialistic affection. This has already been explained. From Brahmā there is Rudra (Śiva), who is in charge of the mode of ignorance or darkness. He destroys the whole creation by the will of the Lord. Therefore all three, namely Brahmā, Viṣṇu and Śiva, are incarnations of the Garbhodakaśāyī Viṣṇu. From Brahmā the other demigods like Dakṣa, Marīci, Manu and many others become incarnated to generate living entities within the universe. This Garbhodakaśāyī Viṣṇu is glorified in the Vedas in the hymns of Garbha-stuti, which begin with the description of the Lord as having thousands of heads, etc. The Garbhodakaśāyī Viṣṇu is the Lord of the universe, and although He appears to be lying within the universe, He is always transcendental. This also has already been explained. The Viṣṇu who is the plenary portion of the Garbhodakaśāyī Viṣṇu is the Supersoul of the universal life, and He is known as the maintainer of the universe or Kṣīrodakaśāyī Viṣṇu. So the three features of the original puruṣa are thus understood. And all the incarnations within the universe are emanations from this Kṣīrodakaśāyī Viṣṇu.
In different millennia there are different incarnations, and they are innumerable, although some of them are very prominent, such as Matsya, Kūrma, Varāha, Rāma, Nṛsiṁha, Vāmana and many others. These incarnations are called līlā incarnations. Then there are qualitative incarnations such as Brahmā, Viṣṇu, and Śiva (or Rudra) who take charge of the different modes of material nature.
Lord Viṣṇu is nondifferent from the Personality of Godhead. Lord Śiva is in the marginal position between the Personality of Godhead and the living entities, or jīvas. Brahmā is always a jīva-tattva. The highest pious living being, or the greatest devotee of the Lord, is empowered with the potency of the Lord for creation, and he is called Brahmā. His power is like the power of the sun reflected in valuable stones and jewels. When there is no such living being to take charge of the post of Brahmā, the Lord Himself becomes a Brahmā and takes charge of the post.
Lord Śiva is not an ordinary living being. He is the plenary portion of the Lord, but because Lord Śiva is in direct touch with material nature, he is not exactly in the same transcendental position as Lord Viṣṇu. The difference is like that between milk and curd. Curd is nothing but milk, and yet it cannot be used in place of milk.
The next incarnations are the Manus. Within one day's duration of the life of Brahmā (which is calculated by our solar year as 4,300,000 x 1,000 years) there are fourteen Manus. Therefore there are 420 Manus in one month of Brahmā and 5,040 Manus in one year of Brahmā. Brahmā lives for one hundred years of his age, and therefore there are 5,040 x 100 or 504,000 Manus in the duration of Brahmā's life. There are innumerable universes, with one Brahmā in each of them, and all of them are created and annihilated during the breathing time of the puruṣa. Therefore one can simply imagine how many millions of Manus there are during one breath of the puruṣa.
The Manus who are prominent within this universe are as follows: Yajña as Svāyambhuva Manu, Vibhu as Svārociṣa Manu, Satyasena as Uttama Manu, Hari as Tāmasa Manu, Vaikuṇṭha as Raivata Manu, Ajita as Cākṣuṣa Manu, Vāmana as Vaivasvata Manu (the present age is under the Vaivasvata Manu), Sārvabhauma as Sāvarṇi Manu, Ṛṣabha as Dakṣasāvarṇi Manu, Viṣvaksena as Brahma-sāvarṇi Manu, Dharmasetu as Dharma-sāvarṇi Manu, Sudhāmā as Rudra-sāvarṇi Manu, Yogeśvara as Deva-sāvarṇi Manu, and Bṛhadbhānu as Indra-sāvarṇi Manu. These are the names of one set of fourteen Manus covering 4,300,000,000 solar years as described above.
Then there are the yugāvatāras, or the incarnations of the millennia. The yugas are known as Satya-yuga, Tretā-yuga, Dvāpara-yuga and Kali-yuga. The incarnations of each yuga are of different color. The colors are white, red, black and yellow. In the Dvāpara-yuga, Lord Kṛṣṇa in black color appeared, and in the Kali-yuga Lord Caitanya in yellow color appeared.
So all the incarnations of the Lord are mentioned in the revealed scriptures. There is no scope for an imposter to become an incarnation, for an incarnation must be mentioned in the śāstras. An incarnation does not declare Himself to be an incarnation of the Lord, but great sages agree by the symptoms mentioned in the revealed scriptures. The features of the incarnation and the particular type of mission which He has to execute are mentioned in the revealed scriptures.
Apart from the direct incarnations, there are innumerable empowered incarnations. They are also mentioned in the revealed scriptures. Such incarnations are directly as well as indirectly empowered. When they are directly empowered they are called incarnations, but when they are indirectly empowered they are called vibhūtis. Directly empowered incarnations are the Kumāras, Nārada, Pṛthu, Śeṣa, Ananta, etc. As far as vibhūtis are concerned, they are very explicitly described in the Bhagavad-gītā in the Vibhūti-yoga chapter. And for all these different types of incarnations, the fountainhead is the Garbhodakaśāyī Viṣṇu.