The Imperial Campaign is perhaps the deepest part of the game, not only do you get to manage a Faction, and lead it to glory, but you can also fight every battle if you so desire! Here are some tips to help you out with the Imperial Campaign mode of Rome: Total War:
I. If you see a city making negative income, do not worry! It could mean that it is just simply paying off your debts, that is, of what you are spending each turn.
II. Near the name of a settlement, you will see a face, the colour depends on how pleased the citizens are of your rule, however. The green face means that they are quite happy with your empire, the yellow face just means they are content, the blue face means trouble, the red face, is the worst, the citizens may revolt from your Faction! If possible, try to keep around the green or yellow face range, and you should have little trouble at all.
III. If you set recruitment on auto manage, you will find that the AI (computer) does dumb things, for instance, the AI may recruit Peasants instead of a unit of Hastati, or Town Watch instead of Triarii, etcetera. I recommend that you manage these aspects of the cities by yourself, as the player is more capable than the AI most of the time.
IV. You probably know about Command Stars, as they appear on your General's traits, and on the campaign map next to him. But do you know what they actually do? It's been said by many players that Command Stars are good because they increase your chance of winning and Auto Resolve battle, but also, on the Battlefield mode of the game, they increase your unit's morale greatly.
V. To Ambush an army, you have to set yours on a forest, and wait, until the enemy comes. Make sure your army is facing the direction you wish for the ambush, and you may be successful, or perhaps not. Do not worry if your ambush is not successful, you could very much still win the battle, but it will be fought as an ordinary battle, instead of the enemy lined up in a column and unprepared.