I think it all depends on HOW you want to conquer the territory -- and bear in mind, that is what you're conquering, not the people.
You have to ask yourself if it's worth it to try to take and hold EVERY city, or if you'd be better served razing some and keeping only the ones that are, say, >5 population.
As a general rule, if you're warring to conquer and grab all the cities, you need garrison troops. I try to land on a square next to a coastal city, preferably one that's got good defenses (forrested hill, jungle, or forrest). When planning the attack, bring defensive troops that'll have good defenses for that specific territory. And don't forget to bring the medics. A pikeman with Combat I and Medic I, and a pikeman with hill defense or whathaveyou can be very very useful. Also, don't SIMPLY build city-raider units for attacks. Sometimes you'll have to fight in open country and those CR3 troops will be worthless against combat I or higher promoted troops (which the AI loves).
Often, I'll take a coastal city and wait for the counter-attack. The AI is oftend dumb enough to send its Stack o' Doom to hit you at this city, so if you're well defended with garrison troops, you can fight him off and severely deplete his military.
You also have to decide how you want to fight. Will you try to decapitate him, cutting off his production capabilities? Will you strike deep into his territory, take his capital, and let him come to you? Or will you nibble away at the edges of his empire, letting him chase you around while you raze his weaker cities?
Personally, I advise going for the high-pop cities ASAP. The AI is notorious for having population 18 cities that all of a sudden become population 9 cities with a large garrison or the beginnings of a Stack of Doom.
Another thing to consider is bringing along a pillaging stack or two, to cut off his strategic resources (ivory, iron, copper, mines, etc.). Remember, the only things you can't rebuild quickly are cottages and their upgraded equivalents.
Also, don't be afraid to starve him out by razing his farms. You'll cut down his ability to whip new troops while his peasants starve.