Seeking suggestions: I want to hunt pirates in Liberty

[Irishacana]

Hey there everyone, I have a successful trader primary character and have saved up over 750 million credits and have a Stork transport. I want to patrol Liberty space as I find there are frequently pirates extorting tolls from defenseless large transports. I have the credits to buy a capital ship but am seeking suggestions!

I was considering going for a Liberty Battlecruiser but am worried it might be too slow to catch the Rogue, Outcast, Lane Hacker or Xeno VHFs I see in the New York System harassing traders.

My other choice which is more affordable is the Thresher from the Bounty Hunters Guild / thé Core which seems to have everything I am looking for. Any suggestions and advice on what ship I should invest in would be sincerely appreciated.

Recap:
Looking to patrol trade lanes in Liberty primarily
Want to hunt down pirates harassing traders
Want a capital ship not a VHF or a Bomber
What faction is best for taking out pirates in Liberty? Liberty Navy or Bounty Hunter Guild?