Gumbolt, I guess that not every player will want to try higher levels of gameplay. Unless I make significant progress in the next year, I probably won't try emperor, ever.
Still it needs a gift to lose on chieftain.
Smallbrain, if you are remaining a barbarian until you can finally adopt free speech and free religion, universal suffrage, environmentalism and emancipation, you will have to wait until your neighbars are bringing them to your cities after conquering them.
The labor civic slavery enables the very powerful tool of whipping. Sure, slavery is awful in real life, but in this game, you can use it to the point of abuse: Sacrificing your (slave) population to build up your infrastructure. Whip, regrow, whip, regrow until you have an army and a city full of magnificent buildings. Use that for research and production, until more civilized civics are available.
If it helps: each time you whip your cities, stop the game, do penance and slave around in the household or garden yourself. Cleaning, ironing, dish-washing, vacuuming, lawnmowing, watering the flowers, whatever. Your household will be the envy of the entire neighborhood soon.
Because, putting it bluntly, if you are able to play a game on a computer and talk about it over the internet? Then you are probably exploiting people of the past and present who built the infrastructure and luxury you enjoy this very moment. But that is a sensitive topic, I'll stop here before I start ranting about how unfair life is...
Um, back to your game: You made a very sensible decision when you decided to grab important pieces of land far away. This strategy is called Rapid Early eXpanding - short REXing. On higher levels, that can keep valuable land and resources out of the hands of the AI enemy. However, you clearly overdid it: You grabbed land too far away. The maintenance cost of cities far from your capital is a lot higher than cities that are overlapping your original capital. If there are resources nearby, you should first aim to get them. Forget about the gold and gem hills twenty tiles away from your capital! Grow your inner ring of a few cities, develop your infrastructure there. Once you did it, and you can build courthouses (which lessen the maintenance penalty of far away cities), you are ready to do a second wave of expansion. If other civs have settled there in the meantime? That's life, look elsewhere.
Now, on war. The AI will keep looking for trouble because it wants to win the game as well. If they decide you are too powerless and/or if your annoy them much (e.g. by having your borders too close to them, or a dozen other reasons), they prepare an army and invade you.
So, as a newbie, just build a moderate army if you don't want to get a surprise visit. Even better, have that army, and once you see that you can't win the game without the juicy land of enemy X, then you should quickly outfit your army with overwhelming offensive numbers (whip helps! also look at what the AI has themselves!) before (!!) you declare war. Then crush them and take their stuff if it is worth it. Destroy other cities if these are crap.
War is hard, of course. But a war done right (and won quickly!) will not kill your economy. Instead, afterwards you have more resources and land and population and hopefully money. The strategy I explained above is just a rough outline of course. Experienced players will run circles around the chieftain level AI even with a smaller army, but as a newbie, you might try brute force and unleash an overkill army of many powerful macemen and trebuchets against a few weak archer/longbow defenders. Once you learned to defeat the AI with overwhelming force, you will love a little bit of war. Just be prepared not to be at the pointy end of the knife.