I'd recommend Federal Combat Bond to start, as you'll only have to fight one pirate at a time. FFA can lead to multiple attacks at once, not something a new player wants to contend with. Practice in FCB. Until you get your ungraded Gimbal Pulse Laser (my first recommended upgrade) just keep at it, taking the free sidewinder until you have enough for the upgrade (and then some in case you have to pay insurance once you upgrade).
Basically, you need to kill about 10 pirates, go to station, sell your current pulse laser, equip the gimballed pulse laser, go back, kill ten more, and get your second gimballed pulse...
Once you're more familiar with flying/combat, give FFA a go, or Contested Space (watch the Anacondas - and if you watch the videos, you'll see the ins and outs of both sides - Go Empire, it's more one on one from my experience, go Fed, and it's easier targets, but more often multiple attackers)... FFA gives 300/kill plus the chance at random cargo worth up to just over 5k (but also brings greater danger - pick off the stragglers, stay out of the middle of the combat zone)