If a city doesn't have a governor, choose "Growth Policy" and take construction and recruiting off auto-management.
Get the highest taxes that will keep public order above 95, maybe 90%. Build arenas when possible. Ignore military buildings, pick the ones that get you money. Don't fill the queue with all the buildings or units you're planning for, that just wastes money; take them one at a time.
Exterminate or enslave the population of all conquered cities, and destroy their temples to replace them with your own. For temples I recomend Mercury.
Start your conquests with Apollonia, then try to take either Thermon or Salona, and if Sparta's still Greek by then take it (use a fleet or tresspass on Macedonian territory). Make peace with the Greek cities when they no longer have anything in Greece that you can conquer, then ignore any Senate requests of blockading Syracuse or Rhodes or Pergamum. If you're lucky enough not to be attacked by Macedonia (try to make them allies), build your forces to attack them.
Don't ignore your navy, as the Greeks can cut you off from your conquests with theirs.
Your Italian possessions are fairly safe now, don't waste too much on defending them.
The western Balkans are a great place for forts, but they're only useful if you plan on a long peace. Otherwise, the armies you use to attack can also take care of any invaders.
When you've conquered enough cities, move your capital to the one that an enemy would have the most problems reaching. As soon as all of Greece is secure, choose a city there. New characters appear in the capital, and if your capital is in Italy you'll have to use a fleet to get them to where the action is (across the Ionian Sea).
Choose your faction heir carefully; don't be afraid to disinherit someone, and keep in mind that future developments might give you better choices. Any character that has more stars than scrolls should be put in command of an army; combat experience can turn him into a great general. Exchange retinue between generals and governors when possible (in some situations, certain characters can be used as "carriers"), as some retinue members are good for governing and some are good for commanding.
I use 3 town watch units to garrison a city, but this may not be the best idea. Your early units are good enough for you, your enemies not having anything much better. Don't waste precious time building the army you can hire on the road. Build better units when they're available, though you'll wait a while for artillery. Always retrain your units where possible.
Never keep your ships isolated. All your possible enemies (for me: the Greek Cities, Macedonia, Thrace, Gaul, Pontus, Armenia, Egypt, and Carthage in an earlier attempt when I cared too much what the Senate said) will have an important naval presence. Groups give you little flexibility, but you can make them almost undefeatable. Retrain your ships when you have nothing for them to do, there's a harbor near the end of your route, or their manpower is really bad. One of the earliest military building you need to be interested in is a shipwright in Italy.
After taking Greece, you have 3 possibilites for expansion (from easiest and poorest to hardest and richest): the western Balkans and then Patavium (if the Julii haven't taken it, it's one way of giving them the finger), Thrace, or Asia Minor and the Mediterranean. When you're done with a theatre, make peace with your enemies there.
Playing like this, you'll still lose plenty of money, but you'll have conquests and trade to support you. I lost a fortune, but I'm now the richest faction, and I've conquered (in chronological order): Apollonia, Thermon, Sparta, Thermon again (my Macedonians allies backstabbed me), Larissa, Athens, Thessalonica, Bylazora, Byzantium, Tylis, Salona, Segestica, Patavium, Campus Getae, Pergamum, and Nicomedia. My capital and largest city is Larissa.