First of all, to answer your side question, yes, there is something that is more particular to Vishnu that both Vaishnavite and Shaivites would acknowledge about him, and that is that he is the god of preservation. That is to say, Vaishnavites would say that Vishnu is the preserver but he is also ultimately responsible for the origination and destruction of the Universe, even though they might be instrumentally handled by other deities. And similarly a Shaivite would say that Shiva is the destroyer, but he is also ultimately responsible for the other functions like creation and preservation. But the one thing that Hindus of pretty much all sects can agree on is that Vishnu is at least instrumentally responsible for preservation, and that Shiva is at least instrumentally responsible for destruction, whatever else might lie behind their power to do so.
This core property of Vishnu, concerning his role in preserving the Universe and its virtuous inhabitants from Adharma, is summarized in a famous verse from the Bhagavad Gita:
To deliver the pious and to annihilate the miscreants, as well as to reestablish the principles of religion, I Myself appear, millennium after millennium.
Now let me tackle your main question, concerning the evolution in our understanding of Vishnu. Note that this isn't about an evolution in Vishnu himself, who has always been the same regardless of human misconceptions, and this isn't even an evolution for certain Trikalajnani sages, who presumably understood Vishnu correctly at all times. But it is true that society's understanding of Vishnu has evolved. Let me explain. (This is an expanded version of what I said in my question here.)
Before the time of the sage Vyasa, people had a very different understanding of which gods were important than the understanding we have today. The Vedic mantras had not yet been compiled into the four books we call the Vedas, but the mantras were still known among men, and they unfortunately led to a skewed perspective on things. Most of the Vedic hymns were addressed to gods like Indra, Agni, Vayu, Surya, Chandra, etc., because they were the most relevant to the Soma Yagna, but people got the impression that those were the supreme gods. It's only after Vyasa composed the Mahabharata and the Puranas that people got a correct view of the importance of Brahma, Vishnu, Shiva, etc. Until then, they were often viewed as minor deities, and people didn't even realize that e.g. Matsya, Kurma, and Varaha were incarnations of Vishnu! (For instance, there's no mention of Vishnu in the story of Matsya in the Shatapatha Brahmana of the Yajur Veda.)
In any case, it's interesting to trace the history of Vaishnavism (Vishnu-worship) before Vyasa came and cleared things up. Vaishnavism came from many different strands, which I'll identify by the name of Vishnu they venerated the most:
Vishnu - There is Vedic Vishnuism, the worship of Vishnu as he's described in the Vedas, which mostly involves his incarnation as Vamana the dwarf. (I give quotes from the Vedas concerning Vamana in my question here.) Because Vamana is known for his taking three steps of land in order to restore rule of the three-worlds to Indra, it was incorrectly assumed that being Indra's helper was the general role of Vishnu. But there are still small references to the other attributes of Vishnu that would become more widely known later on. For instance, Rig Veda Book I Hymn 156 describes his various opulences:
- FAR-SHINING, widely famed, going thy wonted way, fed with the oil, be helpful. Mitra-like, to us.
So, Viṣṇu, e’en the wise must swell thy song of praise, and he who hath oblations pay thee solemn rites.
- He who brings gifts to him the Ancient and the Last, to Viṣṇu who ordains, together with his Spouse,
Who tells the lofty birth of him the Lofty One, shall verily surpass in glory e’en his peer.
- Him have ye satisfied, singers, as well as ye know, primeval germ of Order even from his birth.
Ye, knowing e’en his name, have told it forth: may we, Viṣṇu, enjoy the grace of thee the Mighty One.
Note that the birth is about the birth of Vamana, not Vishnu, but in any case we see here a reference to the power of Vishnu's name. And Rig Veda Book I Hymn 154 describes his role in upholding the Cosmos:
Him whose three places that are filled with sweetness, imperishable, joy as it may list them,
Who verily alone upholds the threefold, the earth, the heaven, and all living creatures.
May I attain to that his well-loved mansion where men devoted to the Gods are happy.
For there springs, close akin to the Wide-Strider, the well of meath in Viṣṇu's highest footstep.
- Fain would we go unto your dwelling-places where there are many-horned and nimble oxen,
For mightily, there, shineth down upon us the widely-striding Bull's sublimest mansion.
And verse 6 explicitly refers to Paramapadam, the supreme abode of Vishnu. The Shatapatha Brahmana of the Yajur Veda describes another property of Vishnu which would become more widely known later on, namely his role as the Yagna Purusha or lord of sacrifice:
Vishnu first attained [the sacrifice], and he became the most excellent of the gods; whence people say, 'Vishnu is the most excellent of the gods.' Now he who is this Vishnu is the sacrifice; and he who is this sacrifice is yonder Âditya.
Note that he is called an Aditya because Vamana is the son of Kashyap and Aditi; it's the same reason that in the Bhagavad Gita, Krishna says "Of the Adityas I am Vishnu". In any case, the fact that Vishnu is the Yagna Purusha would become more important later on; it's the reason that Vaikhanasas and others felt justified in replacing the daily performance of Yagnas with idol worship of Vishnu, because by worshipping Vishnu they were still effectively doing a Yagna.
Narayana - There is the Pancharatra movement, which began with the sage Narayana, an ancient incarnation of Vishnu who was the son of Yama god of death and twin brother of the sage Nara. (Nara and Narayana were previous births of Arjuna and Krishna.) As I discuss in this question, the Shatapatha Brahmana of the Yajur Veda describes Narayana conducting a five-day (Pancharatra) Yagna and then becoming the entire universe:
Purusha Nârâyana desired, 'Would that I overpassed all beings! would that I alone were everything here (this universe)!' He beheld this five-days’ sacrificial performance, the Purushamedha, and took it, and performed offering therewith; and having performed offering therewith, he overpassed all beings, and became everything here. And, verily, he who, knowing this, performs the Purushamedha, or who even knows this, overpasses all beings, and becomes everything here.
The being that Narayana venerated/turned into is described in the famous Purusha Sukta, and the end portion of the Purusha Sukta in the Shukla Yajur Veda (known as the Uttara-Narayana) describes Narayana himself:
- In the beginning he was formed, collected from waters, earth,
and Visvakarman's essence.
Fixing the form thereof Tvashtar proceedeth. This was at
first the mortal's birth and godhead.
- I know this mighty Purusha whose colour is like the Sun,
beyond the reach of darkness.
He only who knows him leaves Death behind him. There is
no path save this alone to travel.
- In the womb moves Prajâpati: he, never becoming born, is
born in sundry figures.
The wise discern the womb from which he springeth. In
him alone stand all existing creatures.
- He who gives light and heat to Gods, first, foremost Agent
of the Gods,
Born ere the Gods—to him the bright, the holy One, be
- Thus spake the Gods at first, as they begat the bright and
The Brahman who may know thee thus shall have the Gods
in his control.
- Beauty and Fortune are thy wives: each side of thee are
Day and Night.
The constellations are thy form: the Asvins are thine open
Wishing, wish yonder world for me, wish that the Universe
Note that in verse 22 Narayana's wives are called "Hri and Lakshmi". In any case, because Narayana peformed a five-night (Pancharatra) Yagna and became all things, people started following so-called Pancharatra texts which gave detailed procedures to worship Narayana. Among the oldest standalone Pancharatra texts we have are the Satvata Samhita, the Jayakhya Samhita, and the Ahirbudhnya Samhita. But there's a Pancharatra text even older than these, and it's part of the Mahabharata! (I discuss the Narayaniya here.) It's called the Narayaniya, and it's an 18-chapter religious discourse between Yudhishthira and Bhishma in the Shanti Parva in the Mahabharata, specifically chapters 335-352. (It's similar to the Bhagavad Gita, an 18-chapter religious discourse between Krishna and Arjuna, and that's no coincidence: the Bhagavad Gita is also considered a Pancharatra text, but it's become so universally accepted by Hindus that people forget its sectarian association.) But it is believed by some that the Pancharatra tradition did not originate in the Pancharatra Agamas we have now, but rather in a now-extinct Vedic Shakha (recension), known as the Ekayana Shakha of the Shukla Yajur Veda, which would have been founded by the sage Narayana. That would explain why the description of Narayana's deeds is in the Shatapatha Brahmana of the Shukla Yajur Veda, and the Uttara-Narayana hymn is in the Shukla Yajur Veda itself. But as far as I can tell the existence of the Ekayana Shakha hasn't been conclusively established.
In any case, the Pancharatra texts advocate the worship of Narayana through Pancharatra Yagnas (apparently free of animal sacrifice); through Karma Yoga (action without desiring a fruit); through recital of the Ashtakshari mantra (Namo Narayanaya), which Narayana is said to have taught his brother Nara; and through idol worship (akin to Vaikhanasas), although this may have originated with the Bhagavata movements.
Vasudeva - There is the Bhagavata movement, which worshipped four forms of god, Vasudeva, Sankarshana, Pradyumna, and Aniruddha. known as the four Vyuha forms. (These are also the names of Krishna, his brother Balarama, his son Pradyumna, and his grandson Aniruddha, but this wasn't recognized at the time.) The Bhagavatas were originally distinct from the Pancharatras, but these groups merged and now it's hard to tell what their unique characteristics were. Idol worship in temples was probably one of them though; Yamunacharya's Agama Pramanya quotes the sage Atri condemning the Bhagavatas along with other Brahmanas who work in temples for money:
The Avalukas, Devalakas, Kalpadevalakas, Ganabhogadevalakas, and fourthly those of the Bhagavata profession are corrupt Brahmins.
(I see five groups, not four, but who's counting?) Most of what we can gleam about the Bhagavatas are in the criticisms of them; for instance, in his commentary on this Sutra and the following Sutras of the Brahma Sutras, Adi Shankaracharya interprets the Brahma Sutras to be criticizing the views of the Bhagavatas with respect to the Vyuha theory.
Krishna - there is Krishnaism, the worship of Krishna due to the various miracles he had performed in his time on Earth, particularly those he performed as a child growing up in Vrindavana and the like. When Krishna's great-grandson Vajra came back to Mathura after the flood of Dwaraka, he promulgated the cult of Krishnaism, focusing on Krishna and his various relatives like Balarama, Pradyumna, Aniruddha, and Samba.
The Bhagavatas and Panchartras eventually realized that Narayana was just an incarnation of the Bhagavata deity Vasudeva, so the two movements merged into one, and then the Bhagavatas realized that it wasn't a coinicdence that the four forms of god they worshipped shared the names of Krishna and his family members. And then finally, when people realized that Krishna is an incarnation of Vishnu, Vaishnavism as we understand it today was born, since people now knew that Narayana, Vasudeva, and Vishnu were all the same god; the Mahanarayana Upanishad summarizes this insight in its famous verse, "Narayanaya Vidmahe, Vasudevaya Dhimahi, Tano Vishnu Prachodayat".
For more information, I suggest you read books on the history of Vaishnavism, for instance Suvira Jaiswal's book "The Origin and Development of Vaisnavism" and S. Krishnaswami Aiyangar's "Early History of Vaishnavism in South India". (Those aren't necessarily my favorite books on the history of Vaishnavism, they're just the first two ebooks I found in my computer's hard drive on the subject.)