Dio Chrysostom, The Second Discourse on Kingship, 15
“Next Philip asked, “But you, Alexander, would you choose to have been Agamemnon, Achilles, or some other of those heroes—or even Homer?” Alexander responded, “Not at all, but I would prefer to be much more than Achilles and the rest.”
Ἐκ τούτου δὲ ἤρετο ὁ Φίλιππος, Ἀλλὰ σύ, ὦ Ἀλέξανδρε, πότερον ἕλοιο ἂν Ἀγαμέμνων ἢ Ἀχιλλεὺς ἢ ἐκείνων τις γεγονέναι τῶν ἡρώων, ἢ Ὅμηρος; Οὐ μέντοι, ἦ δ᾿ ὃς ὁ Ἀλέξανδρος, ἀλλὰ ὑπερβάλλειν πολὺ τὸν Ἀχιλλέα καὶ τοὺς ἄλλους.
Alexander is clearly responding to something he learned from Homer:
“Hippolochus fathered me—I claim him as my father.
He sent me to Troy and gave me much advice,
To always be the best and to be better than the rest.”
῾Ιππόλοχος δέ μ’ ἔτικτε, καὶ ἐκ τοῦ φημι γενέσθαι·
πέμπε δέ μ’ ἐς Τροίην, καί μοι μάλα πόλλ’ ἐπέτελλεν
αἰὲν ἀριστεύειν καὶ ὑπείροχον ἔμμεναι ἄλλων…
“Old Peleus advised his son Achilles
To always be the best and be better than the rest.
And to you in turn your father Menoitios, Aktor’s son, advised:
‘My child, Achilles is superior to you by birth,
But you are older. And he is much stronger than you.
But you must do well to speak and give him a close word,
And to advise him. He will obey you to a good end.”
Πηλεὺς μὲν ᾧ παιδὶ γέρων ἐπέτελλ’ ᾿Αχιλῆϊ
αἰὲν ἀριστεύειν καὶ ὑπείροχον ἔμμεναι ἄλλων·
σοὶ δ’ αὖθ’ ὧδ’ ἐπέτελλε Μενοίτιος ῎Ακτορος υἱός·
τέκνον ἐμὸν γενεῇ μὲν ὑπέρτερός ἐστιν ᾿Αχιλλεύς,
πρεσβύτερος δὲ σύ ἐσσι· βίῃ δ’ ὅ γε πολλὸν ἀμείνων.
ἀλλ’ εὖ οἱ φάσθαι πυκινὸν ἔπος ἠδ’ ὑποθέσθαι
καί οἱ σημαίνειν· ὃ δὲ πείσεται εἰς ἀγαθόν περ.
Those who know me would not be surprised at my answer to Philip’s question. Diomedes, obviously, is the best hero in Homer (or at least the least despicable). Achilles and Odysseus both are problematic–something Plato lets us know in the Hippias Minor
364c: “Homer made Achilles the best man of those who went to Troy, Nestor the wisest, and Odysseus the most shifty.”
φημὶ γὰρ Ὅμηρον πεποιηκέναι ἄριστον μὲν ἄνδρα Ἀχιλλέα τῶν εἰς Τροίαν ἀφικομένων, σοφώτατον δὲ Νέστορα, πολυτροπώτατον δὲ Ὀδυσσέα.
365b: “Achilles is true and simple; Odysseus is shifty and false.”
ὡς ὁ μὲν Ἀχιλλεὺς εἴη ἀληθής τε καὶ ἁπλοῦς, ὁ δὲ Ὀδυσσεὺς πολύπροπός τε καὶ ψευδής
Now, choosing your hero might not be as simple as I have made it. For instance, Homer was clearly prejudiced in Achilles’ favor. And he is really nice to Odysseus, who is a bit of a creep. If you’re more inclined to distribute your character traits along the lines of strength, intelligence, wisdom and charisma, you may want to consider the following.
Hes. Fr. 203
“The Olympian gave bravery to the descendants of Aiakos,
Brains to the offspring of Amythaon, and wealth to the sons of Atreus.”
ἀλκὴν μὲν γὰρ ἔδωκεν ᾿Ολύμπιος Αἰακίδηισι,
νοῦν δ’ ᾿Αμυθαονίδαις, πλοῦτον δ’ ἔπορ’ ᾿Ατρεΐδηισι.
Aiakos was the father of Peleus and Telamon, making him the grandfather of Achilles and Ajax. The descendants of Amythaon were prophets through his son Melampous. The sons of Atreus were Agamemnon and Menelaos.
Of course, this whole question leaves out women altogether, ignoring Corinna’s call: “I sing of the virtues of heroes and heroines.” ἱώνει δ᾿ εἱρώων ἀρετὰς / χεἰρωάδων (fr. 644). I don’t know if there are passages from the ancient world that compare the Homeric women in their virtues. But I do believe that even the best of them are portrayed in Homer merely as instantiations of idealized male desire. And the final note on women in the Odyssey is pretty sour–Agamemnon concedes that Penelope is pretty great, but that she will get slandered anyway. But, I am happy to hear counter-arguments!