Well, you need $80,000 to purchase a War Brig. So I suggest you go looting, this is an easy way to obtain money. Also you can go on material runs, 'mat runs' on your current ship or another ship with a large crew. That'll really help.
Patience is the key, just keep gathering that money. Before you know it, you'll have that shiny new War BRig. And I recommend you upgrade it to Skull and Bones or Copperhead.