You have to keep your people happy, and employed. It would also help to keep a prefecture around too. That blue circle around the buildings before you build, is its area of effect. If you build an Gladiatorial Arena, it's only going to give an entertainment bonus to the buildings inside that blue circle. See what I'm saying? Same goes for food buildings, religious buildings, etc etc unless the description says the benefits go for the whole city.
All in all I believe the following measures are most effective against fire:
As fire is to my knowledge only caused by crime, and quite possibly by having unused buildings or buildings without upkeep, but I'm not sure about that, we want to counter crime.
To counter crime I find it difficult to meet all the needs of my citizens especially when expanding to faraway mines and such, so I tend to keep my residential areas concentrated and keep them fed and entertained and reigiously active, and have slave markets take care of industries such as logging and brickworking. Having equites work the farmers market, butchers shop and bakery increases food saturation, and prefectures seem to help a little, but only in extinguishing fires rather than preventing crime in my experience.
Finally I like to blanket my city with temples of Jupiter to prevent crime near them (with the blessing of Jupiter). There are also several talents that reduce crime, I personally like the Julii family because of the Praetor Peregrinus, which prevents crime when popular. You don't get it until late in the game though. That said I am still a total noob at this game and crime totally takes me out all the time, although I have played through a dozen or so missions. Peace