Disclaimer : i'm not a great warmonger, but i managed to get some Domination victories on Deity with Honor opening.
should i capture, and maybe raze their other cities? ive been letting them live for now, but when i get to the last 1 or 2 capitals i get backstabbed by everybody else that i attacked but left alive.
1. Capture as many cities as your happiness allows. Raze the ones who are happiness sinks.
I think what stormtrooper412 means is don't bother with cities that don't bring you a new unique luxury (unless they are particularly well developed or strategically placed).
If you can wipe a civ before you have contact with other civs (hard to do unless playing Attila), then do it as there will be no consequences. However once you have contact with the other civs, wiping someone will get you a lot of hate. Wiping 2 civs will mark you as the main villain. Taking only the capital and letting them live will keep your relations with other AIs better longer but those civs you let live will hate you because you control their cap. In the early game, you'll have a better diplomatic game and possibly some trade if you let them live, in the late game you'll have more troubles if you let them live (spies couping your CS, pitiful attacks that force you to bring some troupes back). There is no clear winning move. I tend to take cities later (never before XB) and not stop until i've taken the whole world so usually i wipe someone who's close to my mainland and push thought other AIs if i can to get the far away capitals.
2. Puppet until the city is out of rebellion, then annex if happiness allows. Usually you'd want to annex a city on the front lines so you can quickly get a few more (rush bought) units so you don't lose momentum.
And here, i tend to only annex capitals or very good cities and keep the rest as puppets until Autocracy and the Police State tenet (+3
from courthouse). Less cities to check for production, faster National Wonders. I simply spam Trading Posts around those and they give me money to buy more troops as i tend to play HCA when going for dom-V
how much should i grow my capital? captured capitals? and hte other cities?
You capital should be as big as you can afford while keeping a good production. There is no excuse for size 6 capitals by turn 160. You can afford to stop growing if you know you can win before industrial but you need a good civ (Huns, Mongolia, Arabia) on a suitable map (pangaea with not too many rough terrain). A bigger capital gives you more science and will produce better units faster (you won't be able to buy every unit until you have full HCA running) and more
allows you to maintain a bigger army (ever got this red
! in the top bar, your production will drop fast once you hit supply limit). You don't want to work plenty of 4
grassland and get no production of course, but you want to keep growing. Food caravans (or better cargos if you are coastal) can help you grow and work production tiles and they are less likely to be plundered when warring anyway.