Ships & Modules

I'm currently running level 3 missions using my dominix (t2 hardeners/reps, t2 cap modules, t1 med rails, t1 sentries) and its going pretty slow but I'm enjoying it. I would like to improve my skills so that I can do level 4 missions, but I'd also like to get into combat exploration sites and wormhole anomalies where drone focused ships don't do as well.

I need some help figuring out what ships to skill towards that would be able to do this. While missile boats like the drake/raven/tengu seem great for pve, I'm thinking about something a bit more exciting than sitting still and watching my torpedoes slowly head toward their targets. But it seems like lasers and projectiles are not as effective against all damage types unlike missiles since you can change them out easily.

I think that I'd like Amarr ships as using lasers appeals to me, but can they be effective enough against other damage types or would I be stuck doing Amarr (Sansha?) missions and sites? Also, I already have a good start into armor tanking skills so that would help me reach my goal faster. I don't know much about Minmatar ships but I'm open to projectiles or even staying with Gallente and hybrids.

So what ships could you suggest to be my endpoint ( running lvl 4's and combat sites quickly) and what could be some intermediate ships to try out as I am learning the skills to pilot the endpoint ship well? Also, what kind of combat tactics would I expect to use with these ships (ie speed tank but with heavy dos trying to burn down ships quickly).