If you're playing the police for the first time it's easy to get lost on where to begin against your criminal enemies.
If you are playing the higher levels of the game (i.e. Kingping or Godfather) you will want to build more defensive units before conducting an offensive campaign. Your first target should be the weakest of the criminal empire, the Mobsters. They are a small contingent of the map and easy to defeat. Make sure you get to the goods before the Gangs do, as the mobsters have several key abilities that make them powerful.
After you have taken the Mafia (which would seem odd in real life, but the AI is too stupid to properly simulate it,) your next goal should be the Bloods because they could easily become a real thorn in your side. Followed by the Crips, Panthers, and finally the Hawks. You should never persue a broad campaign in higher levels as the gangs can easily outnumber you in their own territory especially when they have barracades (city walls) and you don't.
The police main goal in technology should be Military Weaponry as it will allow you to construct S.W.A.T. units and quickly take the offensive. After that, Flying Equipment should be researched so that you can build Helicopters to increase your speed of attack.