I'm new to the Civilization franchise and was just wondering if conquering early game is worth it. Should I upgrade my civilization and unleash my fury when I have everything unlocked or is there some merit to conquering a civ here or there when still in the medieval era. I ask this because (I'm playing right now) I personally don't see the benefit in just wasting early game units when I can just upgrade everything and unleash hell later on when I have all the fun stuff :)
There is significant advantage to conquering in the early game. Your Civ's power is almost always directly related to the size of your empire, except for the hit to happiness due to size, and potentially income drain if you don't build your economy properly.
Thus, the earlier you get big, the more of an advantage you will have. I tend to try to time my conquering with the advent of new siege units. Usually this means I will go on my first conquering spree when Catapults come along. This is pretty early in the game by any standard.
Trebuchets are a small improvement by comparison, but when Cannons and Artillery enter the game, these are both times to start picking fights.
Artillery in particular start with Indirect Fire and one additional point of range compared to previous siege units. If you get there first and have a strong lead by this point in the game, it's pretty much game over for the AI.
The siege units allow you to down cities quickly and with minimal losses to your army. If you're ahead technologically, taking these units into battle will almost always end in a decisive victory for your side.
Do note that these siege units should be trailing behind whatever front-line infantry is modern at the time you start your attack. By themselves, they're fairly weak and won't stand up to melee attacks.
Once you've conquered a single neighbor, chances are you're going to be ahead in most meaningful metrics. Thus, you'll get to the next siege unit milestone earlier, and can more easily conquer your next foe. This snowball effect means that the earlier you start, the quicker you win.
Finally, if you get to the point where you're playing for score, the earlier you finish the game, the higher your score will be. The fastest way to win is by far conquering the other Civs and taking their capitals. Thus, it's a solid strategy when playing for score to conquer early and conquer often.
Managing your empire in Civ is all about juggling different needs that you can never fullfill 100% at the same time. Ideally you would want to research all technologies, build all wonders and buildings, generate huge amounts of culture and faith, whilst at the same time founding as many new cities as can physically fit onto the map and waging ruinous (for the others) war on all other players/ai. But that is just not possible. Instead you try to cover all the bases as well as you can manage given your current position.
The best time to go to war isn't set in stone, you will have to decide when the conditions are right. The earlier in the game, the easier it is to conquer cities. Especially the enemy's capital gets much harder to take as the game progresses, because it gets bigger and gets better defensive buildings - but also because the enemy will have more space, cities and units between you and it. When you are already falling behind in the early or mid game, it can become increasingly difficult to make up the difference later.
Playing as different Civs and going for different cultures makes a huge difference. Some Peak very early, making early game agression very powerful. Others Peak during the midgame or even later - or they might even not have especially powerful military Units at all, thus their strengths are in different areas.
Overall I try to start dominating my local area right around the time when siege units start to show up. At that stage it only takes conquering the enemy's capital to make them sue for peace, which means wars are relatively short and don't put you behind that much. And since they won't have had much time to grow their newer cities at that point, they will be completely powerless in comparison to you for the foreseeable future.