I think the rock/scissors/paper thing has been done, legion. I know I'm not participating a lot, but perhaps you could move it to 5 levels?
ion is weekest against photon, slightly better against antimatter, balanced against (or even better, negated by) ion, pretty decent against projectiles, and rips the tar out of frequency.
I'm just making up names and relationships out of my butt, but I think that communicates the idea. Yeah, it makes things a little longer to figure out, but 5 levels is still pretty easy to handle, and it becomes more than a rock/scissors/paper game.
My favorite scenario is that a form of energy cannot penetrate a defense made of the same energy, at least not after some serious overloading. Thus ships can have a primary weapon and a secondary weapon. Or perhaps a sliding scale of size. each weapon or defense takes up 1 unit of space. Thus, the smallest ship has one 1 unit of space, an can choose either a weapon or a defense matrix. The largest ships can have10 spaces, allowing them to have a defense and a weapon of each type. Or you can reduce that value to 6 or 7, stating that ships large enough to have weapons useful for their size and have more than that many types of weapon/defense requires too much energy to be maintainable.
I think about the system I liked for Star ship conbat best, "Star Warriors" and it was pretty simple, though. One type of shield, just varying damage for weapons. The beauty of that system was maneuvering. I recommend adapting something like that and adding some complexity to the weapon/defense mechanics.