The title says it all, I’m working on a board game modeled around this time period but I can’t represent every valuable commodity in game, so I’m focusing on the six most significant ones!
Spitball answer:
The major goods by value and volume, that were traded on the Mediterranean probably did not change much between the early periods of antiquity and the early middle ages. With that huge postulate in mind, here are my own guesses for the major commodities of that period, drawing heavily from The Roman Empire: Economy, Society and Culture, by Garnesy.
Major commodities in overland and sea-borne trade during most of antiquity, included, but were not limited to (in rough order by volume)
By far, the largest commodities by both mass and value were grain and olive oil, with everything else being a much smaller proportion of the market. If you wanted to, you could split the "grain" category into wheat and barley.
I think this is a neat question, and hope someone more qualified to answer it than me comes along!
That's a little tough. The Carthaginians would essentially trade in anything that turned a profit. You can get a sense of their contemporary reputation via the stereotypical portrait of a Carthaginian trader in the comic play Poenulus, by the Roman comic playwright Plautus (c. 254 – 184 BC). Hanno, the trader, in Act Five gives a list of all sorts of gimcrackery he has on offer.
That having been said, if we must narrow the goods down to six, and for your purposes I expect you want a little variety, let's start with tin. Crucial for making bronze. The Carthaginians had a stranglehold on the straits of Gibraltar, so if you wanted Cornish tin, you had one choice (they also monopolized Spanish tin). Also from Spain, they had silver, always welcome in trade. In worth, both are significant.
Locally, they were rich in grain, which they exported (if was in large part their means of paying Rome its indemnity after the first Punic war), so for volume, also significant. (Add to this olive oil and wine - amphorae may make for better visuals than grain, if that's a consideration.) Slaves. Fine textiles, particularly those died purple with murex shells. They also sold a variety of manufactured goods.
Slightly off topic, but worth a mention is Josephine Quinn's recent book the recent book, In Search of the Phoenicians (Princeton). I've not read it yet, but as Carthaginians are basically Phoenicians who went west, it sounds like it's worth a look.
Good luck with the game.