So, one part of a game that is easiest to talk about tends to be the really early part. With that in mind, I thought I would make thread about choosing which of the two cards drawn at the beginning of the game should be your starting meld.
This list deals with base, two player Innovation.
With 15 Stone Age cards in base, there are 15!/(13!2!) opening hand possibilities, which is 105. Rather than have 105 entries, I'm going to present a priority list that creates guidelines that handle all 105 cases. The priority list doesn't necessarily represent some openings being stronger than others, in fact, I don't care all that much about figuring out whether Clothing/Pottery is a better opening than Wheel/Tools, I only care about whether I meld Clothing over Pottery and whether I meld Wheel over Tools. This is much more actionable information.
So, to interpret this list, for any opening hand, you try to select the highest priority opening meld you can. If an exception is marked on that priority, then you meld according to the exception.
We should keep in mind that playstyle is a major factor in the decision, but at the same time there are some choices that are of such different strength that playstyle won't matter, and there are some choices that fit more playstyles than others.
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Priority 1: Sailing
Priority 2: Domestication, except in favor of Masonry
Priority 3: The Wheel
Priority 4: Clothing
Priority 5: Metalworking
Priority 6: Masonry, except in favor of Writing or Pottery
Priority 7: Mysticism
Priority 8: Writing, except in favor of Tools
Priority 9: Pottery, except in favor of Tools
Priority 10: Oars
Priority 11: Agriculture
Priority 12: Archery
Priority 13: Tools
Priority 14: Code of LawsPriority 1: Sailing
Sailing gets you 2 standard actions for the price of one. Only two Stone Age cards can force you to share this astounding power, and those cards happen to be unwanted melds early on anyway.
You'll notice that the first three cards mentioned all have dogmas that unconditionally or almost unconditionally cause you to perform 2 of your standard actions at once. These effects are powerful because they help you get access to new dogma effects rapidly, and they help you gain icon control. Scoring dogmas can be powerful too, but the player who is developing his board with 2 for ones can often share scoring effects.
Priority 2: Domestication, except in favor of Masonry
Domestication also gets you a 2 for 1, but an order of magnitude more cards can force you to share your mastery of animals.
Masonry is a close call, but I think Masonry should be melded instead of Domestication, because an opening hand of Domestication/Masonry makes it very unlikely you can perform an unshared Domestication that doesn't cover Domestication. Masonry has better icons and Monument prospects with Domestication in hand.
Priority 3: The Wheel
The final reliable 2 for 1. You meld Domestication instead of Wheel because Domestication is generally a better dogma. While Archery or Oars could make you wish you selected the 2-for-1 card with more icons, for every Archery or Oars opening there's several castle-less openings where Domestication can run freely and untamed (Do you see what I did there?)
Priority 4: Clothing
The alphabetic C means that you can meld the other card from your opening hand if it helps you block a 2 for 1. And while Clothing is a 1 for 1, it scores you lots of free points. Even when Clothing doesn't give you 6 points in the first few turns, it usually at least forces your opponent to spend time melding differently colored cards to block you, often ones he didn't want to spend actions melding.
Priority 5: Metalworking
Deciding to meld Metalworking over Masonry was a close call, but my logic is this: while Metalworking does a pretty crappy job at finding you cards that work with Masonry, it does a pretty good job at finding cards that let you make use of Masonry without melding it: Pottery and Agriculture.
Priority 6: Masonry except in favor of Writing and Pottery
Masonry has good icons that block the castle 2 for 1's. But if you draw it with a card with no castles, the future looks bleak for getting good usage out of Masonry's dogma. Writing and Pottery have useful dogmas and are worth sacrificing castle icon dominance, Pottery does so in part by giving you the option to pitch Masonry for points and give up on the castle arms race entirely.
The other castleless cards have dogmas that are weak enough that you would rather meld Masonry for its icons, though.
Priority 7: Mysticism
Good icons, same as Masonry. The dogma isn't powerful early on, but the icons are powerful early on. A hypathetical triple castle card with "C: No effect" might be ranked right below this card, actually.
Priority 8: Writing, except in favor of Tools
Drawing 2's is marginally better than drawing 1's. Tools can fix the issue with Writing and Tools sharing a color by throwing Writing away, though. A play that is even more powerful when you consider that your Stone Age opponent will get to the end of the Stone Age stack, only to discover you put a Writing there that will be utterly useless now that he can draw 2's with Domestication now..
Priority 9: Pottery, except in favor of Tools
Pottery ranks below both of the other blue cards because the main strength of its icons is blocking Clothing, which you can't block very effectively with two blue cards in hand anyway. But it beats everything else because it blocks Clothing and has a useful dogma (More useful than Agriculture, early on).
Priority 10: Oars
Oars blocks Domestication. It also has an okayish dogma early on if you share it.
Priority 11: Agriculture
Agriculture blocks Clothing. It's also alphabetically first, giving it a "scouting" feature that synergizes with its dogma: you get a chance to see whether your opponent opened Sailing or Writing, giving you a heads-up on whether you should block by melding a Code of Laws or Tools from your hand, or instead take draw actions with the intention of pitching those cards for points later.
Priority 12: Archery
Archery blocks Domestication. Its dogma is totally useless early on, though.
Priority 13: Tools
I think some would put this much higher, but I don't think they should, 3's are much weaker early on, and returning three cards is costly. However, if you make it all the way down to this priority, the other card in your hand must be pretty weak, so it hurts much less to trade it away for a 3.
Priority 14: Code of Laws
Melding Code of Laws over City States gives City States more surprise factor.
