Basically they are traders of the Mediterranean. Here is literally pretty much everything REH had to say about their culture:
Argos: “They were characteristic Argosean Sailors, short and stockily built. …” from Queen of the Black Coast pg. 124
“… He was well aware of the enmity which existed between the pirates and the Zingaran buccaneers. The pirates were mostly Argossean sailors, turned outlaw; to the ancient feud between Argo and Zingara was added, in the case of the freebooters, the rivalry of opposing interests. Both breeds preyed on the shipping and the coastal towns; and they preyed upon one another with equal rapacity.” from The Black Stranger pg. 119
“The barbarians who overthrew Acheron set up new kingdoms,” quoth Orastes. “Where the empire had stretched now rose realms called Aquilonia, and Nemedia, and Argos, from the tribes that founded them. The older kingdoms of Ophir,Corinthia and western Koth, which had been subject to the kings of Acheron, regained their independence with the fall of the empire.” from The Hour of the Dragon pg.88
“Argos was at peace; laden ox-wains rumbled along the road, and men with bare, brown, brawny arms toiled in orchards and fields that smiled away under the branches of the roadside trees. …” from The Hour of the Dragon pg. 183
“From the men that worked the fields, from the garrulous old men in the inns where he slaked his thirst with great leathern jacks of foaming ale, from the sharp-eyed silk-clad merchants he met upon the road, Conan sought for news of Beloso.
Stories were conflicting, but this much Conan learned; that a lean, wiry Zingaran with the dangerous black eyes and mustaches of the western fold was somewhere on the road ahead of him, and apparently making for Messantia. It was a logical destination; all the sea-ports of Argos were cosmopolitan, in strong contrast with the inland provinces, and Messantia was the most polyglot of all. Craft of all the maritime nations rode in its harbor, and refugees and fugitives from many lands gathered there. Laws were lax; for Messantia thrived on the trade of the sea, and her citizens found it profitable to be somewhat blind in their dealings with seamen. It was not only legtimate tradethat flowed into Messantia; smugglers and buccaneers played hteir part. All this Conan knew well, for had he not, in the days of old when he was a Barachan pirate, sailed by night into the harbor of Messiantia to discharge strange cargoes? Most of the pirates of the Barachan Isles- small islands off the southwestern coast of Zingara- were Argossean sailors, and as long as they confined their attentions to the shipping of other nation, the authorities of Argos were not too strict in their interpretation of sea-laws.” from The Hour of the Dragon pgs. 183, 184
“He entered the city unquestioned, merging himself with the throngs that poured continually in and out of this great commercial center. No walls surrounded Messantia. The sea and the ships of the sea guarded the great southern trading city.” from The Hour of the Dragon pg. 184
“Publio sat at a carved teakwood desk writing on rich parchment with a golden quill. He was a short man, with a massive head and quick dark eyes. His blue robe was of the finest watered silk, trimmed with cloth-of-gold, and from his thick white throat hung a heavy chain of gold.” from The Hour of the Dragon pg. 185
“It was long and narrow, a typical trading-ship of the southern coasts, high of poop and stern, with cabins st either extremity. Conan looked down into the open waist, whence wafted that sickening abominable odor. He knew it of old. It was the body-scent of the oarsmen, chained to their benches. They were all negroes, forty men to each side, each confined by a chain locked about his waist, with the other end welded to a heavy ring set deep in the solid runway beam that ran between the benches from stem to stern. The life of a slave aboard an Argossean galley was a hell unfathomable. Most of these were Kushites, but some thirty of the blacks who now rested on their idle oars and stared up at the stranger with dull curiosity were from the far southern isles, the homelands of the corsairs. …” from The Hour of the Dragon pgs. 197, 198
“What ship is this?” Conan demanded.
“The Venturer, out of Messantia, with a cargo of mirrors, scarlet silk cloaks, shields, gilded helmets and swords to trade to the Shemites for copper and gold ore. …” from The Hour of the Dragon pg. 198
“… The Argosseans were strong, sturdy, fearless like all their race, trained in the brutal school of the sea. …” “What ship is this?” Conan demanded.
“The Venturer, out of Messantia, with a cargo of mirrors, scarlet silk cloaks, shields, gilded helmets and swords to trade to the Shemites for copper and gold ore. …” from The Hour of the Dragon pg. 200
Nothing he writes indicates they were Ancient Greeks. Quite the reverse. Their culture is far later technologically. And the Aquilonians aren’t Ancient Romans either. Technologically and culturally they are far more Medieval. But, as usual, FC gets it wrong or deliberately decided to do it differently for reasons that mystify me.