The thing with textual transmission is that the books that we consider Classics of Latin and Greek literature, were copied again and again throughout the ages precisely because people appreciated them. For the most parts, the Latin and Greek texts and languages did not need to be rediscovered and deciphered, because there were always people who knew about them, sometimes fewer, sometimes more. Some works actually were lost for centuries, because they were not transmitted continually for various reasons, but were rediscovered because archaeologists found papyri with those works on them in ancient landfills. This is true for Sappho or Menander. There are also some that existed as medieval manuscripts in old monastery libraries that nobody bothered to seriously look at for some hundred years. The Roman historian Velleius Paterculus was rediscovered this way when in 1515 Beatus Rhenanus found an 8th century manuscript in an Alsacian monastery.

So generally yes, people in antiquity and later on appreciated these works when they were still somewhat"fresh", that's why have them today and call them "Classics". Although, the main reason why some works were kept, was because they were deemed useful in the classrooms to study grammar and rhetorics on them, not because they were a particularly interesting read.

You were asking about their popularity "when they came out", and that is really difficult to say. We don't have the feuilletons and book reviews of that time that discussed the newest arrivals; we don't have statistics about book sales. When other ancient authors reference them, we today can tell that these references were still understood, which means they were popular at that later author's time.

What I personally don't know is if there was some kind of "van Gogh", whose manuscripts only circulated and became famous after his death. The closest I can think of is Aristotle, whose extant works are not those he published for wider circulation (the "exoterical" scriptures), but only for internal use for the lectures and handbooks in his school ("esoterical" scriptures). These manuscripts much later found their way to Rome and were then compiled and copied in the 1st century BCE. The exoterical scriptures were still known at that time.

So about how works were received upon publication: The Athenians had drama contests at their festivals to Dionysus and we've got lists of the names of the winners. In the tragedies and comedies that we have today, we very often also have annotations made by early classicists, that state which place the pieces made in the competitions.

These lists of winners give us often enough the names of the four Attic playwrights we still read today (Aischylus, Sophocles, Euripides, Aristophanes), but also of many others that were very popular in their time, but we only have fragments of their works now. Like Kratinos, Eupolis, Phrynichos.

If by "disregarded" you mean, that we know of them and have text but just don't like them anymore: While it may be true that classicist in general don't do research about the works they personally don't like or find interesting, it is not at all true that we would purposefully let certain works fall into oblivion. Not everything is a masterpiece, but one man's trash is another man's treasure; and every bit of writing is of scholarly value. Even Philogelos' collection of jokes.