This may be a tall order but having recently immensely enjoyed Robin Lane Fox's Alexander, I'm left remembering a remark he made in the preface to the effect that there are very few ancient figures that are appropriate subjects for historical biography due to the paucity of contemporary sources. One exception he notes is Cicero, who is remembered through his voluminous letters and speeches. My question is what other ancient historical figures or events in ancient world history are supported by a plethora of contemporary source material, if any?
I'm not an ancient historian (and I'd be glad if one came and corrected me!) but I do have some knowledge of the period.
The only figure comparable to Cicero I know of would be his younger contemporary Caesar. Just like Cicero, we have plenty of works by Caesar himself surviving, and he was written about a lot by his contemporaries (including Cicero!). Only a fraction survives, but the last decades of the Roman Republic are, as far as I know, the period best documented by surviving contemporary sources in the Ancient period. As a result, it's probably (by far) the most written about period of Antiquity too. Tom Holland's Rubicon is a good narrative introduction to the period in a similar sort of style to Lane Fox.
Close seconds would probably the the early Imperial period and late 5th century BC Athens, but these, if I recall correctly, have much more diffuse sources and rely on epigraphy and archaeology to supplement the single-authored contemporary texts (Thucydides, Livy, Tacitus). As such, they're much harder to relate to a specific person or event.
There is no Greek we know as much about as we do about Cicero. In fact, some of the most famous figures of Greek history (Solon, Kleisthenes, Leonidas, Perikles) are actually quite poorly attested. For many important people we rely on the late testimony of Plutarch (2nd century AD) for biographical information. We just have to hope that he did his homework and didn't let his moralising intentions override his integrity as a writer of history.
Some of the figures we know most about are actually names that may not sound familiar: Agesilaos, Alkibiades, Dionysius of Syracuse, and Demosthenes the orator. In the latter case this is mostly because of references to his own life and actions in his court and assembly speeches (and those of Aischines). I hesitate to include Sokrates in this list; he's probably the one featured in the largest volume of contemporary sources, but since the two main strands of this evidence (Xenophon and Plato) use him as a mouthpiece for very different ideas, it's hard to say how much we actually know about him.
In later periods, we know quite a lot about men like Philopoimen and Herodes Attikos. To my knowledge, the most comprehensive biography written about a Greek-speaking historical figure is that of Apollonius of Tyana.