The title of the thread was the opening, which I define as the first 50 to 100 turns, say until 1AD at the outside. By that time Ill have 6-8 cities or so, maybe 10 techs, a wonder & will be in Monarchy.
I think La Fayette is right on target -- for the first two or three moves or so (but not ten to twenty) place your first city in a good location. Sometimes the blinking initial spot is only a space or two from something truly optimal (have you ever placed a city with tow specials only to find that by moving one more space you could have had another two whales (but now never will?) Yes, the initial site could be ideal, but there is nothing wrong with: 1) moving a couple of spaces and opening up a hut with the initial settler, and sometimes 2) Ill road a shield grassland space, move another space and then start my capital (which could make a difference of a number of turns of initial research.)
What to build right off? I like a searcher or two, partially for the nearby huts, partly for ideal city locations, partly to meet the neighbors. Depending upon the terrain, I may go with a horse (if it was granted as a starter tech), but the warriors are SO cheap, that is it hard not to use them as 1) police; 2) fodder; 3) cheap searchers. When they are far away, they may uncover huts that could yield NONE units, as well as cash & other wondrous gifts.
After my first searcher or two, the next build is a couple of settlers -- although if Im playing at a high level and this city is truly in a sweet location, maybe only one settler (to be followed by a Wonder). -- I want three or four cities near each other to help provide for the common defense, and to ease the movement of camels later on. Circa the third or fourth city being founded, one of them will have started a wonder.
Research plan -- 60% science, 40% cash; Ceremonial Burial, Alphabet, (Off Tech), Code of Laws, Monarchy. Then revolt & change the allocation to 70%/30%. The Off Tech, could be Bronze Working or Writing -- both have strong merits. Sometimes, Ill come across a free tech from a Hut, which could mean that Ill skip the off tech & move forward through to Monarchy with four techs researched. Ive also discovered that if one starts with Bronze as a free tech, then one can postpone the Off tech awkwardness & get to Monarchy with four techs researched (theres been some study as to the tech availability -- usually one a third are available at any time).
Next research target -- Write or Bronze, looking for the intermediate goals towards Philosophy and Trade (Myst, Lit, Curr). I find that Ill have to research all the techs to Philosophy to get the free tech, but if I deviate from that path, Ill miss out at a deity and sometimes even emperor. At King & below, Ill go for Trade before Philosophy.
Avoid wars until Tactics, but if there is too much pressure, get some vet elephants after Monarchy & establish a domain of at least a dozen decent cities to work with -- ie, if you only have space for five-six cities on your side of the island, then research Poly (build a barracks & start a settler -- switch to an elephant & with two or three of them, clear out the other civ in your way. dont make this the only thing going on, however -- continue building your first wonder & researching at max level.
First wonder? I usually go for Colossus in my best location, may switch to Hanging Gardens (and back again) if I think that I can nail two of the ancients in the same spot. Usually I can get one or two at deity, 1-3 at Emperor, 3-5 at King, and 6-7 at Prince. but then again, I usually make a strong effort at building wonders over making extra settlers and growing faster
As far as units go, Ill have a couple of warriors out searching, some of the free units from huts doing the same, but only one or two offensive units back home for barbarians -- once I have a dip or few, one stays home, a few may be located in the SSC as pre-camels (just in case for Col), and a few may be out searching. The militia (warriors) are posted where needed, and maybe a couple of defenders in key cities or at the fringe. I seem to be increasingly careless that some of my core cities are actually empty.
Infrastructure? Most of the cities will have temples -- the SSC gets everything when it is not putting up a wonder. Other cities wont have anything else until later in the game.