The Barzini family, They are the strongest family that you will face in-game.
If you are just starting out Avoid them at all costs until you have gained a respect level of at least 25+
The majority of Barzinis are underbosses and cappos, these ranks have a higher hp value than other family's members of the same rank. Most likely they will be armed to the teeth with tommyguns, shotguns and magnums.
Starting a mob war with them is not the best idea...
Dealing with them is best to be done last when you are fully equipt with upgrades and skill points used.
The way you can identify them is with their green attire.