This brings back memories:
http://forums.civfanatics.com/showthread.php?t=271411
Get as many cities as you can, and do whatever possible to have 1) enough happiness to grow cities 2) enough commerce/gold to actually pay for your cities and 3) enough units to stay alive.
It took me a long time to get used to having 10 cities or so in the BCs or early AD's on emperor and immortal, and even longer before I comprehended just how many maps it's possible to get that many peacefully (with a rush is a little easier because you get a gold buffer).
As for techs, expanding sufficiently will often drag your slider to dangerous levels. I prefer expanding until it is 0 now, staying just above the threshold of strike. If your cities are growing and some are working cottages, you'll pull out eventually.
What to do in the mean time? The answer is specialists. Use the scientists off a library whenever you can afford it. This does two important things:
1. Nets you an early great person, which is very useful
2. Provides some minimal (or with pyramids significant) beakers towards your next tech.
Try to research techs that allow you to trade for multiple other techs. Aesthetics is frequently good for this, code of laws also can be for the early tech tree. Both are much better targets than math, currency, feudalism, calendar, or machinery in typical games, as the AIs will tend to get those early. Note this does vary somewhat game to game...keep an eye on the tech trade screen.
Other than that, as your cottages grow and you are able to trade for

resources and build/whip some courthouses, you should take off with a lot of cities.
If you get boxed in, your only true options are typically an early rush or a bulb-fest to renaissance units and abusing the temporary advantage with superior units via drat, the whip, and/or mass upgrade of CR maces to rifles etc. On the bright side, you won't have the slider lower, but getting more cities is usually the better call.