I've been playing on Emperor for the past 4-5 years, and here's my starting thoughts/strategies.
* Food and growth is important, but defending your starting city is more important.
* Soldiers are expensive to maintain, only train what you need (though you will need a fair amount to compete with AI)
* Starting location and resources matter significantly
* Settling many cities fast is a sure way to bankrupt yourself into a death spiral. But if you don't settle a spot of land, the AI likely will.
* Always have a vision and a plan.
My usual approach:
1. My first 3-4 researched techs are about getting a food source, immediately followed by woodworking to train militia. If I have crops nearby, great. I study agriculture, and then immediately go for tool making and wood working. If there are cattle/sheep/pigs, then I instead go for animal husbandry first and only then go for wood working. If I don't have crops nearby in the starting city radius, or if there is wine, I use the wheel to get to animal husbandry instead of agriculture. If there are neither crops nor livestock nearby, GG. Game's over and time to start again.
2. Military is expensive, only train what you need. Warriors become obsolete very fast but militia can be used for a while to come, so training warriors early on is a waste. Going straight for militia will allow you to build a decent defense before any threats (barbs or aggressive civs) show up without wasting build points or cash on useless warriors.
3. Military is expensive, only train what you need. The basic 3-strength archers are nowhere near as good as the 4-strength archers that are unlocked with Iron Working. Upgrading them is insanely expensive, and trying to replace them one by one is time consuming, wasteful, and too much micro-management. And as mentioned above, militia are a good defensive unit already. So skip the 3-strength archers and hold out for the 4-strength ones. Only research archery if you need walls, the buff to buildings/improvements, or are desperate to improve you civ strength ratio.
4. Workers are the first thing I build, even before growing the city. Once I unlock woodworking I'll be training 4-5 militia, and I don't want to pause on that to build a worker. The 40 or so turns to woodworking is the grace period where I can build non-military units, so that's how I use it. I usually build two workers, and if I still have a few turns left to WW, I'll build a scout.
5. Use your military to control the surrounding territory and reduce the barbarian spawn. Barbarians can start overwhelming if they're allowed to hang around, and recovering from this can be difficult. You want to use your militia to prevent their spawn as much as possible and hold them back at choke points. Easier said than done, of course, but a constant goal non-the-less.
6. The primary concern early game is having a good city for building military. You'll need it. After that, it's all about economy. Find the cities with the best potential to improve your economy, allowing you to maintain a strong military while also maintaining decent research. Economy economy economy.
7. After researching WW, I'll usually get the early mining tech, the stoneworking tech, and possibly weaving and/or the one that shows hemp if I think I might have some nearby. At this stage I want to get an idea of where to build my next 2 cities, since I likely won't have more than 3-4 cities for a long while, and I want to make those cities count. So getting an idea of the available resources can be helpful.
8. I don't play things turn by turn. I figure out what I'm going for and make a beeline for it. If I don't have bronze and am short on military production, I shoot straight for Iron Working. If I need to buff my economy, I go straight for trading. If it looks like I might want 5-6 cities based on resources, I will go for a religion to try and maximize happiness and the value of these cities. And if I have a lot of coast, I'll prioritize the The Great Lighthouse and/or the The Colossus (if I have bronze). Either of these wonders can be the critical element that leads to a successful early game thanks to the economy boost. And the +4 gold/turn from Great Merchants is an easy way to afford more military without impacting research. Economy economy economy. Great Prophets (+6 gold /turn) are even better at this, but their wonders might not have as much of an impact at the economy wonders, so it's a trade off. Building the Great Bath can put you off to an amazing start, but there's a good chance an AI civ will beat you to it, and the gold compensation isn't worth the production loss. Building Pyramids can be useful because the unlocking tech should be an early research anyway, the AI doesn't prioritize it, and it can make building The Great Lighthouse/The Colossus almost guaranteed. But skip Pyramids if angry barbs force you to spend a lot of time building units, since an AI will likely get to it first. Stonehenge is also a good option if you think you'll want to expand to 4-5 cities quickly, but the AI can be competitive about building it.
9. The only exception to the beelining in the above point is to unlock the 4-strength recon units. They're going to be critical for dealing with barbs and the other civs that will eventually try to invade you (there's always one).