There is no point doing attacks piecemeal as a barracks in the city will heal all the damage you have done to the units that weren't killed. When all the defenses are gone you never have to worry about not having movement left with any of your units as you simply activate the fortified defender and claim the city. After that it is very hard to break through 3 or more musketeers in a city as there just isn't the firepower in the units. Conscription makes it highly impossible. Sea power is a great way to limit the computers ability to wage war on you if you are on a different land mass to them, and all the coastal cities of your enemies are easy prey with a good fleet.
Air power can be good, especially if they are too heavily entrenched with ground forces.
Bombers can be used to surround a city when attacking to limit the amount of partisans that appear when it is taken and stop them movement of enemy ground troops through the squares they occupy. They stand little or no chance if they are not. One way to ensure that your force is well trained is to leave the building of your army to a few select cities with good production. I even do this very early in the game, so that all my city defenders are veteran and will not lose to barbarians that frequently appear. This makes the military producer suffer from lack of infrastructure, but I compensate for this by buying its needed buildings.