My training is as a Latin and Ancient Greek philologist and I'll answer with a view to those languages.

On the final evaluation grammar is an artifice that we choose to use because it allows us to effectively discuss language. Students of Latin have used Cicero as an exemplar for the proper use of the language since antiquity (Quintillian, for instance), but Ciceronian Latin was never representative of all Latin. Instead, it attains and establishes an elite register that probably diverged from colloquial Latin in important ways. For instance, we know from the graffiti of Pompeii that Latin's case (nominative, genitive, etc.) and gender systems were already starting to break down in the classical period. In the prior case, this is probably because of the historical development of the preposition in Indo-European languages. If prepositions began their development as simple adverbs, which is especially evident in earlier texts like the Homeric corpus, then the rigid and correct use of case endings was important for averting confusion; however, by the classical period prepositions had begun to appear with greater frequency in static association with a noun. At this point, the preposition is starting to do all of the work (indicating direction and locality) once contained within the case-ending. This leads to the idea that the case-ending was already starting to become redundant in Cicero's time, and certainly thereafter, yet there is no reflection of this in the corpus of his writing. Cicero's Latin is an excellent Latin, but it is one Latin.

As far as general use of the language goes, we do have excellent fragments of a number of ancient grammarians, which provides us with some basis for thinking about how a native speaker exposed to the "Many Latins" of his time might have seen the language. Have some Varro (VI.5):

"Nunc quod ad eas res attinet quae in tempore aliquo fieri animadverterentur, dicam, ut haec sunt: legisti, cursus, ludens; de quis duo praedicere volo, quanta sit multitudo eorum et quae sint obscuriora quam alia. Cum verborum declinatuum genera sint quattuor, unum quod tempora adsignificat neque habet casus, ut ab lego leges, lege; alterum quod casus habet neque tempora adsignificat, ut ab lego lectio et lector; tertium quod habet utrunque et tempora et casus, ut ab lego legens, lecturus; quartum quod neutrum habet, ut ab lego lecte ac lectissime: horum verborum si primigenia sunt ad mille, ut Cosconius scribit, ex eorum declinationibus verborum discrimina quingenta milia esse possunt ideo, quod a singulis verbis primigeniis circiter quingentae species declinationibus fiunt."

"Now I will describe what pertains to those things that are considered to be conducted in some time, such as these: (1) 'You read', (2) 'Having been run', (3) 'Playing.' I want to say two things first about these: how many there are and which are more obscure than others.

There are four types of declined word; (1) that which denotes time and does not hold a case, such as leges [[you will choose]], lege [[choose]] from lego [[I am choosing]]; (2) another that holds case but does not denote time, such as lectio [[selection]], lector [[selector]] from lego [[I am selecting]]; (3) a third that holds both case and time, as legens [[a selecting person]], lecturus [[a person about to select]] from lego [[I am selecting]]; (4) a fourth that holds neither, such as lecte [[select]], lectissime [[most select]], from lego [[I am selecting]]. The original forms of these words number around a thousand, as Cosconius writes, [[but]] from the declination of these words fifty-thousand divisions are thus possible, because from each original word around five hundred forms are created through declination."

When we look at the language today, we are incapable of saying in every case how that example relates to the average "guy on the street," but we can say that it is an example of one "good Latin" because we still have Latin/Greek writers like Varro who were deeply concerned with language.

Sources: Woodcock's Latin Grammar Varro VI

Appendix:

I want to build on the idea that there could be multiple correct ways to express the same idea without appealing, as I have above, to the split between vulgar and aristocratic Latin. For this we're going to look briefly at inscriptions from the small Greek city of Oropos. Because of its size and awkward position between Boeotia and Attica, Oropos frequently flipped back and forth between the influence of different hegemonic powers (Athens, Thebes, etc.). The local dialect of Greek that the Oropans used seems to have more affinities with Attic Greek than Boeotian Greek, but for much of the 3rd Century BCE Oropos was part of the Boeotian League. Let's look at proxeny decrees produced in Oropos in the same period, one Boeotian, the other "Oropan:"

δεδόχθη τοῖ δάμοι· Ἀγεί[τ]ορα //
[Πα]ρμενίωνος Μεγαρεῖα πρόξενον εἶμεν κὴ εὐ- // [εργ]έταν τῶ κοινῶ Βοιωτῶν κὴ αὐτὸν κὴ ἐσγόνως // [κὴ εἶμ]εν αὐτοῖς γᾶς κὴ οἰκίας ἔππασιν καὶ ϝισο- // [τέλια]ν κὴ ἀσφάλειαν κὴ πολέμω κὴ εἰράνας κὴ τὰ // [ἄλλα ὁ]πόττα κὴ τοῖς ἄλλοις προξένοις κὴ εὐεργέτης.

"The people have ratified that Agetor son of Parmenion of Megara become proxenos and benefactor to the League of the Boeotians, himself and his descendants, and that they have the right to possess land and a house and the same tax burden as the Boeotians and protection in war and peace and all the other things that the other proxenoi and benefactors possess."

δεδόχθαι // τῶι δ[ή]μ̣ωι· Οἰνόφιλον Φι<λοποί>μενος // Κρῆτα πρόξενον εἶ̣[ναι κα]ὶ εὐε- // [ρ]γέτην τῆς πόλεως [Ὠρ]ωπίων καὶ // [α]ὐτὸν καὶ ἐκγόνους καὶ εἶναι αὐ- // [τ]ῶι γῆς καὶ οἰκίας ἔγκτησιν καὶ ἀσφά- // [λε]ιαν...

"The people have ratified that Oinophilos son of Philopoimen of Crete become proxenos and benefactor of the city of the Oropans, himself and his descendants, and that he have the right to possess land and a house..."

So, the English translation is more or less the same, and the meaning is almost identical in Greek, but there are a number of morphological and lexical differences:

(1) In Boeotian there is δεδόχθη τοῖ δάμοι for (Oropan) δεδόχθαι τῶι δήμ̣ωι (2) "" there is εἶμεν (the infinitive "to be") for (Oropan) εἶ̣ναι (3) "" there is κὴ ("and") for (Oropan) καὶ (4) "" there is ἔππασιν ("possession") for (Oropan) ἔγκτησιν

The texts share a template and are in communication with one another to that extent, and yet they include these and other differences. This at least suggests the ability of two different "Greeks" to coexist in one community under different political circumstances.