I like the list except for Yam, while I have enjoyed a little renaissance with them lately and they are a great tool rush civ you can do better with other tool rush civs and still have an iron.
Baby, near the bottom, oh grasshopper what you need to learn. This civ has a number of great strats. They are a good tool tower/slinger rush civ. Bronzes depends on the situation. You can go comps if gold seems appropriate or CA's and camels. You can gobble up land and not give it back in bronze quite well because of the unit mix and towers. The CA/Camel mix is always great. In iron, heavy cats and all Gov. Center upgrades don't hurt (They DO need better pit upgrades, their scythes don't compare). They have legions, HA, and the second best priests in the game. Pick your poison, a VERY flexible civ and one I play often as a pet civ.
Second to add to your list is roman. Learn how to tool rush and you'll never do it with any other civ than shang. In bronze while the lack of CA's hurt the cheap towers and use of Chariots assisting is usually more than adequate to get through the age to iron. They have a great iron but go legions all the way. While you can get HC's you don't have engineering.
The third addition I would make is mace, a weaker economy but better bronze than your minoan choice.
For my own personal style I would rank mace and roman ahead of minoan and especially against minoan. With Roman full tower slinger rush and with mace a slinger rush to keep it fair followed by hoppers with bronze sheild=120 compie shots...ouch!
Anyway, your original lsit of civs was good if you want to get off the beaten path you need to try some other strats that take a bit more work but once mastered are very effective.