Im a little slow at the start -- I build roads to my next city (not optimal). At start, search for no more than a few turns, plant a city in a good location -- dont be too concerned about optimal placement for the first couple of cities (although I do, again, it is not best play). Build a warrior to search (cheaper & faster out the door than a horse) build a second warrior (if at Deity or Emperor) for police, followed a settlers for a second city. The settler should march to a good site (found by the first warrior -- that is his primary job). I prefer that I have a roaded grassland to work, so my cities sometimes get a slower start, but keep in mind that the cities wont get too large, maybe size 2 or 3 for a while, because they will be pumping out settlers.
Assuming a tech path to Monarchy, the only infrastructure youll need for a while is a temple for some cities, maybe a barracks in your civ, and after Colossus for your SSC, a library & marketplace. The SSC should be located in a great place, but a good place will do -- note that even at Prince level, the AI will start wonders around their 3rd or 4th city, so that pressure should help gauge whether or not youre too slow at the start.
Plan B is to build many micro cities close together, say a space apart, with the intent that these villages will never get beyond size 8. In fact for much of the game theyll lurk around size 2 -- thus not needing ANY infrastructure. With this Infinite City Sprawl (ICS), the little cities can produce military units if desired, camels and dips, extra settlers for even more micro cities. The rationale is these each contain a fully developed square when created (road & irrigation for free) plus the working citizen -- a good deal compared to the time a settler takes when roading and irrigating. With ICS as an active plan, the Hanging Gardens serves very well, meaning that those cities size two or less in the core of your empire may not even need defenders.
I still havent fully adopted the ICS strategy, but for me, Ill end up with a SSC, a few secondary wonder cities, and smaller cities. During the early game, these smaller cities will be around size 3-5 or so, and the secondary wonder cities limited to size eight until I get Mikes, and size 12 until I take out another civ or two.
Even if Im planning on going to AC, I like to have a couple of civs conquered to make sure I have enough room, say 50-60 cities or so, about two to three times the size of number two.
But the thrust of your question was early game research. My first goal is an improved government (typically Monarchy), and I often get a free tech by being the first to Philosophy en route to my second goal of Trade. Meanwhile expand your civ, and expand your search (for huts, new city sites, and neighbors, both friendly and otherwise). when trade is in hand, send a camel over seas to some foreign civ demanding a product from your SSC -- the return is both coins (nice) and beakers (VERY nice). Once you start to see how 150 beakers for a camel, or 200 beakers for a camel play into your science, youll want to push this envelope a little farther. (In the latest Game of the Month, I was getting 1,000 to 2,000 coins and beakers per truck late game consistently, trading from New Zealand to North America
getting a tech a turn for many turns in a row.) And the trading pays off even better after you switch to Republic (en route to Democracy).
