I am the most experienced with Civ 5, so I'll focus on that, but as I recall from 4 there were no significant downsides to taking over enemy cities except that city maintenance was based on distance from capitol, so far off enemy cities would cost more.
In Civ 5, there are a lot of upsides and downsides to capturing enemy cities. The most immediately obvious downside is that occupied cities add a lot of unhappiness to your empire, but in addition they will cost money to maintain buildings while providing none for the first few turns when they are in revolt, and capturing cities will quickly lead to high warmonger penalties. The last downside is important even if you plan to take over every person in the game, since you don't want the whole world to declare war on you at once until you can actually take them on. In general, the fact that the city will be in revolt and useless for the first (population after capture * tourism reduction) turns after capture means that unless you plan on razing the city (which requires you to annex it), you should always puppet new cities at least until they are out of revolt. You do not gain the double unhappiness penalty from puppeted cities. You may decide further to wait until you have enough gold to buy a courthouse outright to take away the occupied penalty from your city before annexing it. The extra maintenance is basically unavoidable, but I have rarely been in a situation where it had a significant impact on my empire's economy so it is probably insignificant in most situations. The warmonger penalty is based on the number of cities your enemy has left, so one strategy is to take as few cities as possible before taking the enemy's capitol (and thus knocking them out of the game for practical purposes), and then letting them live until you no longer care about what other nations think of you. Another is to declare war alongside other civs and to strategically take declarations of friendship, which reduces the warmonger penalty you gain from taking cities. Civilizations which have denounced a civ similarly care less when you take that civ's cities, so attacking universally-hated civs can allow you to expand while minimizing the warmonger penalty.
All of this helps you decide how to capture cities, but you can also help your empire prepare. City population and number of cities both increase unhappiness based on a rate (as in, the more cities you have and the more citizens you have, the more unhappiness you get) whereas happiness increasing modifiers are generally static (+4 per luxury, +2 for buildings, etc). With this in mind, try to build happiness buildings in all cities, and try to capture enemy cities that have new luxury resources first (as long as the resource is improved and in your borders you get the happiness from it and can trade it, it does not have to be worked). When choosing allies (or more cynically, the people you plan on killing last), choose people who have lots of luxury copies that you don't have access to so you can keep that modifier high. In general, before you take a city try to estimate how much unhappiness it will add to your empire, and try to avoid going below -10 (which is the point where rebels will spawn in your territory). With this in mind, going for policies which increase your happiness is always a great investment, since each one offsets some of the unhappiness from capturing new cities.
All this said, it is almost impossible to completely or even significantly dominate the world before you have access to ideologies, mainly due to being unable to effectively mitigate unhappiness. All three are suitable for world domination, but Freedom is probably the weakest of the three for this purpose and I wouldn't recommend it unless you are trying to challenge yourself. With that in mind, here are where the other two excel for world domination:
Autocracy is pretty much the "out of the box" world domination ideology. It has a lot of troop bonuses and some happiness increases, as well as a tier 2 perk which adds happiness from courthouses and makes them faster to build, reducing the amount of time an occupied city will be unhappy and allowing all captured cities to further help mitigate their own unhappiness. In addition, Prora (its unique wonder) is the single highest happiness building in the game, giving 1 happiness per two social policies taken, this can easily be +10 happiness as soon as you get it (plus the free +2 it gives).
Order is less about improving troops and more about making a ton of them. It has the best happiness policies, you are almost guaranteed to have a monument in every city and combining Workers Faculties and Young Pioneers will make new cities start producing lots of hammers (and thus new buildings or soldiers) within very few turns of capturing them. Its unique wonder, the Kremlin, is pretty meh but fits with the theme of making a lot of troops, allowing the city it is built in to make tanks twice as fast.
To sum it up, the main two things you should worry about are your happiness from taking new cities, and your diplomatic relations with other nations while they can still gang up and defeat you. The second is dependent on keeping track of who hates who and allying yourself with a few other civs while you take over other civs they don't like in the early-mid game. The first is about estimating how much unhappiness you will gain from taking a city (minus any happiness it will give you, from eg new luxuries and wonders).
Last but not least, a few wonders to consider working toward early game (by late game you should probably be letting your opponents build wonders for you):
Terracotta army - can be useful if you think you got to the tech for it first, but it doesn't offset the increased maintenance, so be careful.
Pyramids - Will be helpful in repairing pillaged tiles in captured cities and getting them back on their feet faster, and having the free workers can be a nice early game boost.
Statue of Zeus - kind of nice, but honestly you may as well use the hammers on soldiers and build it later if it's still available (it often is). Honor isn't particularly useful unless your civilization synergizes with it anyway.
Notre Dame - absolute must have, the +10 happiness is around 3 free city captures.
As I'm about to post this, I realized that I haven't talked about religion, which is a topic in itself and very useful for offsetting happiness penalties. In addition, I intentionally haven't gotten into specific strategies because this answer is already really long, I'd recommend that the OP come up with some more specific questions and post them separately if they'd like more specific answers.