The BHG are, to a greater or lesser extent, the police: they're friendly with House police and hostile to criminals. They serve as the police in the outlying systems, where the Houses have no control.
Vs the Corsairs and Outcasts, neither side is much stronger (not least because it's easier to program
). The BHG tend to have more conflict with the Corsairs though, as they operate in more BH systems.
The first two ships in the BH line are both excellent choices for a player starting out, either in the story or online. However, many people do not consider the Hammerhead to be worthwhile - as for a relatively small amount more you can get your hands on an Eagle or Sabre.
It's debateable how good BH weapons are. They tend to have longer range than equivalent class/type weapons, but sacrifice damage. They're a good choice for the safe player who likes to keep his distance. However, IMO, there are better weapons available for the same prices. This kind of thing will vary from player to player. Pick up a BH ship and some guns, see if they suit your playing style. Just experiment