Yeah, game start can be exceptionally difficult; it's not really balanced yet.
My suggestion would be, start with a wolf class frigate. (No, I don't remember which answer to what question gives you that option - but you can hit escape at ship selection and try again until you find it.)
Then, go into refitting, and make the following changes to weapon groups:
group 1: both harpoon racks, alternating fire, autofire turned off - this is the weapon group you'll be using manually.
group 2: graviton beam, linked fire, autofire turned on
group 3: tactical lasers, linked fire, autofire turned on
Now, in combat against fighters, the tactical lasers will mostly just kill them; your only concern is keeping shields angled reasonably - or turning shields off if you're in close combat with a wing of Broadsword fighters; their kinetic guns won't do that much damage to armor, but will overload shields in no time flat. Ideally, you want to fire off a harpoon or three at broadswords when they're just approaching being on screen (at maximum zoom-out) - that will at worst distract them a bit, and at best take out one of the three fighters before it's in range to attack you.
Against enemy frigates, use strafing to aim (hold down shift, hit any turning key, and you'll rotate towards the mouse) - this will let you accurately aim the graviton beam, even when its firing arc isn't displayed. You'll need to let up on shift in order to turn shields to absorb salamander hits, but otherwise this should work fairly well. Use harpoons primarily against high-flux, overloaded, or venting targets; the two unshielded ships you'll fight are likely to either dodge (hound), or shoot down your missiles (buffalo II) - though in the later case you can just spam-fire four to six missiles for a nearly-guaranteed kill.
And, lastly, the ship system. It's a short range teleporter - moves you a fixed distance in the direction you're currently flying (not the direction your ship is pointed). It also shuts off shields (so be sure to bring shields back up quickly if needed), and will re-orient your ship to face towards nearby enemies. This is the crown jewel of the Wolf frigate, and why I suggest the wolf as the optimal starting ship when learning the game. Missiles incoming and you have your shield pointed the wrong way? Teleport. Enemy ships starting to get into flanking positions? Teleport. It's basically a limited-use get-out-of-jail-free card; the charges are limited, but usually regen fast enough to be available when you need them. (Oh, and it's also nice when trying to chase down fleeing enemy ships.)