My character race is Gallente Gallente and I've been using hybrid turrets with antimatter ammo so far because my cruiser (Thorax) gives a damage bonus on them but I'll shortly be upgrading to a battle cruiser for level 3's then a destroyer for level 4's
You do know the destroyer is weaker than cruisers and battlecruisers.
Flying level 4's you should really be in a battleship (preferably maurauder), or a strat cruiser.