I said I'd give Cayvie some earlygame advice, so I'll post it here. Note I've only played twice, and a lot of this is based on what didn't work first time and what did second time.
Don't consider this hard rules, this is mostly advice that will help your civilisation grow without getting stuck in a rut.
Firstly, the important things in the first few turns are resources, science and food. Food is only used for making extra people, so it's probably the least useful by a small factor or those three. Increasing your population and either science, resources or food is a good first move.
Happy faces, culture production and military can be left until a few turns in - one discontent worker will keep you for happiness, until you've increased pop 6 times, which is pretty likely going to be most of age 1. And early culture can be good, but if your advancement falls behind as a result, you can be fighting an uphill battle for the rest of the game. Military can be important from as early as the third turn, if someone lucks into drawing and using an aggression, but you can probably leave it one or two turns more than that.
Don't underestimate the action cards. They take two civil actions over two turns to use, but they can help accelerate you towards what you need.
Think carefully about your choice of leader. You can only take one leader per age, so while a poor Antiquity choice can be fixed if a better age 1 leader comes out soon, a bad age 1 choice can leave you lagging for 1/3rd of the game.
Military actions are really good. Even if you rarely use all of them, drawing extra military cards (and holding more) can be a huge factor. It gives you more control over future events, an easier time building your military, more likely to grab bonus cards, etc. Even if you aren't going military very much, extra military actions are great.
Wonders are expensive, but very strong. Think carefully before starting one. The age A wonders for example take 6 resources to build, that's about 2 turns worth of resources. If you can spare that, go for it. If not, don't.