There was a huge industrial production of fish products, including Garum that was exported to all the Mediterranean Sea. We can see there the “cetárias” were the fish bowels rotted and dried with the sun and salt.
Garum does indeed sound atrocious. In his book 'The Great Sea', David Abulafia says a Garum factory was excavated at Barcelona. He also indicates that the invention of Garum was credited to the Carthaginians. It seems the trade was mainly eastward moving from factories on the Iberian peninsula and the North African coast (it may not have been confined to this area). It was also said in this book that a lot of amphorae found in Corinth may have contained this foodstuff, perhaps arriving from Carthage.
A lucrative source of profit for Cyrene was the medicinal plant called silphium. It grew wild and proved resistant to transplanting elsewhere in the Roman world. Its root could be pickled and its leaf eaten, and it was used as a laxative and as an antiseptic. In fact, silphium came to be considered as wonder medicinal plant, with many claiming it as an aphrodisiac to a cure for chills. It was so important to the economy of Cyrenaica that it was depicted on the coinage of that region. The plant has never been definitely identified, but it may have been related to fennel. The plant probably became extinct during the reign of the Emperor Nero.
Roman exotic luxuries were probably the item with the largest profit margin
I mentioned silk , China was the only possible source ,
I would think India was probably the intermediary ,
this doesn't exclude adventurous Roman or Chinese merchants trying to cut out the middlemen
Many have addressed the rather wide first question. Although there's been a tendency over the years for ancient historians to ignore or even dismiss the economic reasons for ancient players' actions on the basis that is a modernist view, those reasons existed nonetheless. A better way of approaching that question is from the perspective of what still drives geopolitical action today: resources and their control; nothing has altered over the millennia. Once looked at from that angle, the most important tradeable items were grain, precious metals (and iron) and, often, timber.
Some of the most important players of the ancient world were unable neither to feed themselves nor finance/supply the raw materials for their military activity. Rome and Athens are two classic examples. Rome was in no position to feed itself and the granaries of the ancient world often dictated policy. Thus we have the early relations with Egypt and Rome's sensitivity to perceived threats to Ptolemaic independence. Despite the Carthaginian question, Sicily's rich harvests, too, were not to be ignored
Athens is, perhaps, a more clear example. Filthy rich (by Greek standards of the time), she was able to finance hitherto unheard of trireme fleets. That money, though, came from the empire she'd acquired by stealthy and not so stealthy means. If one were to look at the distribution of the concentrations of both attic pottery (shards) and coinage, one soon sees a pattern: precious metals; grains; timber. That is no coincidence. The establishment of Amphipolis was not for any social experiment - as Athens' later desperate efforts to reclaim it show - it was for the adjacent silver mines and timber (something which dictated her policy towards Macedonia as well). The same can be said of her efforts in Egypt and Cyprus mid-fifth century and Sicily/Magna Graecia in the late 330s/early 320s (grains). As Peter Green archly observed (Diodorus Siculus Books 11-12.37.1, Greek History, 480-431 BC, The Alternate History, 228, n 167):
An empire without bread starves. A naval empire without timber rapidly becomes a contradiction in terms [...] To control a trade route was no less important than controlling the source of the import that traveled it.
He's dead right. These were the basic important trade commodities of power and it doesn't take too long to think of Roman and other examples. If you traded these commodities you were at once both well off and rather concerned about the power politics of your time.
Of course, there were other, less critical but no less important staples (wine, oil, etc.). Garum, mentioned much hereabouts, became an industry to itself under Rome whose citizens, apparently, were addicted to it. It had been around for some time but Romans acquired a taste near unquenchable for the stuff. It's not hard to imagine Mafia-style syndicates waring for control of its distribution. As an addict of good 40n Vietnamese fish sauce, I can fully understand...
once Sparta had taken control of the grain sea lanes by their victory at the goat river battle
Athens had the choice to starve or surrender
they choose to starve , then surrendered
"Without her protective fleet, Athens was vulnerable to attack. After a lengthy siege, the city surrendered unconditionally in 404. Many of its citizens were dying of starvation.
The state that had started the war as the most powerful in Greece had been reduced to nothing "