EVE New Citizens Q&A

I'm a fair way into the SoE Epic Arc Missions. I'm flying a Vexor which is a Gallente Cruiser specialising in Drone Deployment.
I started the game with the tutorials, then I focused on some missions and attaining my Core Basic Competency. Now I'm doing the SoE line and have focussed on maximising the effectiveness of my Drones. I can tailor my drones to the mission at hand with regard to their size.

My advice to you, based off my fresh experience, is to use your Destroyer to absolutely carve it up. My Catalyst was so much fun, and I find myself in it from time-to-time. In fact, I have no idea why I'm using a Vexor. I guess I just find it easy to quantify my success by referring to my ship size. lol!
Read up on the info tabs of particular ships as it will have skills/certs that are recommended for it's effective operation.
Study some fittings from other peoples ships to see what's effective, and why they chose it.

Edit: I'll just add, that you're right by wanting to move up in ship size I believe; It will make it much easier. And you'll know once again when you're ready for a Cruiser.