Skill Discussions

For PVE, have you tried artillery? They'll have the range you need, but lower DPS. Otherwise, go back to missiles.

PvE in Minmatar ships relies on falloff bonus'ed ships like the Machariel. There aren't a ton of great of ships in their lineup for PvE.

Syndicate is Serpentis rats so I'd suggest training a Gallente platform like the Ishtar or Vindicator. Tengu and Gila work as well.

I find that the thing that catches allot of long term missile users up when switching to guns is that they have forgotten about transversal velocity. With missiles it doesn't matter as much, you just orbit at range and then press F1 etc. With turrets you have to shoot with the lowest transversal, sometime this means that you don't orbit but rather fly at various angles to what you are shooting to reduce the angular transversal velocity for you guns so that they hit more often.

Going from missiles to autocannons will definitely be an adjustment range-wise. ACs do great damage up close, but for a lot of missions, artillery will serve you better. The caveat is that with their much lower tracking, once smaller ships get under your guns they can be a big problem. Be sure your drone skills are decent (at least 3s on the supports, and T2 light drones if possible), and they'll be your close-range protection.

Learn to switch between AC and Artillery based on the mission and projectiles will work just fine for you. I'd suggest getting friendly with Pyfa/EFT for figuring out the crossing point for a given ship/skillset. If you're aiming for L4s, at the top end there are range-bonused hulls (Vargur, Machariel) that can get away with sticking with ACs for missioning.

All that said, I think pulse lasers are pretty popular these days (though I don't have personal experience with them). If you're willing to switch systems again, maybe do a little research on those?

Your question is a bit general I get no sense of preference pvp or pve.
In any case since I don't know what you deem more important I would say go with projectiles, it is more cap forgiving and needs the least gunnery support skills of all guns.
I made a post on this in the skill discussion section.
You won't need controlled bursts which is 2x multiplied, as well as being able to skip out on sharpshooter a 2x multiplier to 5 or 4.
Lasers and hybrids need a more balanced support make up, but are much more needy to begin with due to cap dependance which is big.
Projectiles gives the most bang for buck out of all weapon systems, just be mindful that the cruiser line is a bit busted for minmatar, BC and BS are nice though dont know about frigs but with the gunnery tiericide this matters not, just jump straight to whichever ship you need guns for.
But projectiles are an easy climb up.

I was like you (started caldari/missiles) and before i truly started flying amarr i trained all my gunnery support skills to 4 and the small ones to 5. seems like a lot, but i saved myself the pain in the ass i read about lots of people having...

I don't know much about minmatar guns, but i flew the naga back when fhubs were beast and now i use the paladin and i like it way more than the tengu..

good luck buddy,
tl:dr train support skills first!

well i am all ears if you would care to enlighten me :)