Yes, reading the 'classics' of a particular period is well worth a go, if you have something specific you want to gain from them. The easiest way to find out what those books are is to find a good modern textbook on the topic at hand, with a bibliography (it should be an annotated one so they give you a sense of what to expect). Or, if there is a lecturer in the department with a focus on the area you're interested in, you can find out when their office hours are, go and talk to them, and get your questions about what is and isn't worth reading that way.

Reading your question, it's hard to get a sense of whether you mean the classic bits of historical writing on a period, or just the original bits of written primary source material. Or indeed just history written by Romans and Greeks? Whatever the case, and particularly if you're approaching the primary sources without prior experience, it can be well worth reading some of the main works on that period. That gives you an idea of the questions people have asked the sources in the past, so that you can come away from them having learned a bit more.

For Classical Greece: Herodotus, Thucydides, Xenophon, Plato's "apology"

For Macedonian hegemony: Arrian, Curtius Quintus Rufus, Plutarch, and Diodorus

I also recommend literature on Demosthenes famous speeches to the Athenian assembly. He addressed the assembly many times and they give a great insight into the popular feeling regarding Philip of Macedon

Romance of the Three Kingdoms, is a fantastic Chinese classic that's been cautioned for centuries as one to not be given to the devious. As sly as Art of War. As dramatic as Game of Thrones. As cited throughout East Asia as a source of universal wisdom as any comparable western classic.

Those standard classics are all excellent reads, but be careful about getting burned out: many of the translations can be excessively dry. If you want something a little bit more laid back, I highly recommend Ovid's stuff (most especially Ars Amatoria and Metamorphoses - if you want good translations of either, let me know), as well as Apuleius' The Golden Ass. Not only are they quick and easy reads, but they also provide a huge amount of context into daily life that you don't get as much as you would from the "macro level" histories. For example, here's a snippet from Book III of Ars Amatoria:

How near I was to warning you, no rankness of the wild goat
under your armpits, no legs bristling with harsh hair!
But I’m not teaching girls from the Caucasian hills,
or those who drink your waters, Mysian Caicus.
So why remind you not to let your teeth get blackened,
by being lazy, and to wash your face each morning in water?
You know how to acquire whiteness with a layer of powder:
she who doesn’t blush by blood, indeed, blushes by art.

You make good the naked edges of your eyebrows,
and hide your natural cheeks with little patches.
It’s no shame to highlight your eyes with thinned ashes,
or saffron grown by your banks, bright Cydnus.
It’s I who spoke of facial treatments for your beauty,
a little book, but one whose labour took great care.
There too you can find protection against faded looks:
my art’s no idle thing in your behalf.
Still, don’t let your lover find cosmetic bottles
on your dressing table: art delights in its hidden face.
Who’s not offended by cream smeared all over your face,
when it runs in fallen drops to your warm breast?
Don’t those ointments smell? Even if they are sent from Athens,
they’re oils extracted from the unwashed fleece of a sheep.
Don’t apply preparations of deer marrow openly,
and I don’t approve of openly cleaning your teeth:
it makes for beauty, but it’s not beautiful to watch:
many things that please when done, are ugly in the doing:
What now carries the signature of busy Myron
was once dumb mass, hard stone:
to make a ring, first crush the golden ore:
the dress you wear, was greasy wool:
That was rough marble, now it forms a famous statue,
naked Venus squeezing water from her wet hair.

We’ll think you too are sleeping while you do your face:
fit to be seen after the final touches.
Why should I know the source of the brightness in your looks?
Close your bedroom door! Why betray unfinished work?
There are many things it’s right men shouldn’t know:
most things offend if you don’t keep them secret.
The golden figures shining from the ornate theatre,
examine them, you’ll despise them: gilding hiding wood:
but the crowd’s not allowed to approach them till they’re done,
and till your beauty’s ready banish men.

But I don’t forbid your hair being freely combed,
so that it falls, loosely spread, across your shoulders.
Beware especially lest you’re irritable then,
or are always loosening your failed hairstyle again.
Leave your maid alone: I hate those who scratch her face
with their nails, or prick the arm they’ve snatched at with a pin.
She’ll curse her mistress’s head at every touch,
as she weeps, bleeding, on the hateful tresses.
If your hair’s appalling, set a guard at your threshold,
or always have it done at Bona Dea’s fertile temple.
I was once suddenly announced arriving at some girl’s:
in her confusion she put her hair on wrong way round.
May such cause of cruel shame come to my enemies,
and that disgrace be reserved for Parthian girls.
Hornless cows are ugly, fields are ugly without grass,
and bushes without leaves, and a head without its hair.