Archipelego maps provide the best chance for early civ building with little need for an army.
I can play regent + level and have only 1 defensive unit per city... if I see someone starting to get mad at me or gearing up for war, then I will try to beat them to it.
Certain civs, like Germany and Aztecs (the Militaristic ones in general) are hell bent on war. Any of them will war with you (except mayby India) if they have a 2:1 army advantage or better.
Anyways, go with the flow but don't leave yourself naked if there is a chance of an attack.
The enemy will rarely go for internal cities first... they will attack your border towns first... those therefore need the barracks, walls (if small strategic/resource towns only) and best defense - 2 defense and 1 offense minimum.
Once you control an entire continent and have RR to every city then you can go back to 1 per city and have a fast response force (usually I put them in my capitol) of another 1 per city... so if you have 12 cities, your fast attack force would be 12 units all lumped in your capitol... you wipe the enemy out wherever he lands instantly using RR.
BUT that wont usually earn you peace... You should have transports handy lined up to the closest enemy coastal city.
They attack you, the very same turn you should have 9-12 units (your task force) in the boats, then turn after they land, turn 3 they take an enemy city. By this time you have a second task force complete or near complete to either a) continue the campaign, b) leave them home if you get peace.
Then you keep that taken city as a fortress... get the culture up there asap... get walls and barracks there right after... In about 10 turns using cash you should have: temple, library, walls, barracks.
Now you can stand pat there - if the enemy re-declares war, they will 90% likely go for their old city... which is your strongest point of defense
OR you can say - heck I got all these military units, and I got a strong foothold here... time to launch a wipeout campaign... then you go for the kill on them.