What if the country in question is far away? In my current game I'm at war with Germany but they are halfway around the world. If I take their cities wouldn't corruption be too high? I guess I could always switch to communism but I think I'd prefer to stay republic.
But if the nation is far away, then they can't hurt you in return either, the AI is absolutely terrible at D-day invasions, so you won't build up WW from them.
You don't get WW just from being at war, you only get WW from:
# losing units when you attack (winning the attack does
not give WW)
# being attacked (even if your defender wins)
# losing units when being attacked.
# having units in enemy territory for a whole turn. (the amount doesn't matter)
# having enemy units in your territory for a whole turn. (the amount doesn't matter)
# Losing cities (this will cause a very big hit, but you shouldn't lose cities vs the AI though, if you know what you are doing.)
If the enemy declares war on you, either because you refuse a demand, or because some civ buys them in an alliance, or because they do something plain crazy and random. (they sometimes do) you get negative WW. meaning, you get
happiness! (except if this is a result from a failed espionage mission by you)
So if a far away civ declares, they basically give you a nice gift!
The corruption of far away cities doesn't bother me, every city adds something to you empire, you can always irrigate everything and hire specialist (the output of specialist can not be modified by any factor, including corruption) you just have to make sure there are no structures in the city that cost gpt upkeep, because they don't add anything in return in corrupt cities.
An empty city doesn't cost you any upkeep, like in civ4, only city improvements do.
I always fight my direct neighbors first, but not because I like to avoid corruption, just because it makes for shorter supply lines, and thus faster results. I won't start fighting far away civ until the civ in between us have been conquered, then the far away civ will become my new neighbor, thus my next target.
You could send a few units to hurt the far away enemy his economy, but doing so is extra work and extra planning, it also adds WW for being in enemy territory (negating some of the War happiness), and it makes your unit susceptible to being attacked and being killed. (adding more WW) Though these should be only small amounts.