The current meta is range + sublight speed.
Some computers let ships stay at their max range, and shoot at the ennemies while they can't fight back.
This is especially true for carrier computer, and also true for artillery computer in most cases (Sometimes the computer doesn't select the right weapon for the range check and you end up too close).
So the best weapon, in no particular order, are missiles, strike craft and X-slots.
Concerning X-Slots, arc emmiters are better 90% of the time (the 10% left are Cetana and multiplayer).
Concerning missiles, go for the S-Slot archeology ones if you can, M slot otherwise (The standard S slots have more damage than M Slot, but are far weaker against PD).
Carrier will be stronger than everything else most of the time. When the enemy has a lot of PD's or strike craft of his own, you might prefer X-Slots (against fallen empires or Gray Tempest for example).
Concerning fleet composition, I prefer mono fleets. I am sure you can mix ships without issue, but I don't think you would get any benefits by doing that.