It's funny really because most of my Civs are usually hitting their stride right around the time you get Riflemen. I tend to have Civs that start slowly but then peak in the Middle ages, and then again in the Industrial and Modern ages.
In the early game, I tend to ignore Stonehenge and The Oracle (going a Creative leader helps or if not going a Civ that starts with Mysticism and founding Bhuddism or Hinduism) and instead, after settling 2-3 cities, concentrate on getting 2-3 workers out there, temples, granaries, and libraries in every city (access to fish, corn or wheat plus slave whipping helps massively here as does forrest chopping). Beeline to Alphabet to enable tech trading and ensure I'm keeping par with every other Civ. In short, I always tech-trade like mad. You start to get a feel for researching niche techs which the AIs will want. In fact, you can safely Beeline to certain techs and be safe in the knowledge that you'll get anything you miss through trading.
Again, I don't make the early Wonders a priority and keep the bare minimum (i.e. an archer, axeman and spearman) to defend each city. Instead, I concentrate on workers: build cottages on any square that wont serve better doing something else (i.e. most plains and grassland). If the city is desperately lacking in production, I might build a couple of workshops and likewise if it is desperate for food I might build a farm or two but, on the whole, cottage spam is the order of the day.
I also avoid early war at all costs as I find that it almost always severely disrupts my tech development leading the civ to fall off the pace. Instead making MONEY is the main goal for my civs: Banks, Grocers and Markets in every city. Plus money per turn for spare resources and money from founding religions. By the time you can rush by money, your Civ with have built up over 10,000 gold easily. And from there, provided you've not gotten into any costly wars, you should be set to win --
unless this happens! 