The most effective is mortar.
Depends on your mission. Arty covers a much wider area for a bit longer than mortars, mortars fire more concentrated and quickly over a smaller area. If you want to kill dudes in one area, mortars work well. If you want to deny your enemy an area for a while, artillery works better.
Rockets don't ever seem to be that much more effective than artillery at killing things, but are over in 10 seconds and have a long cooldown time. They don't get much done.
Really what they should have done is given the commander a set number of fire-missions for each arty type per map, rather than this unrealistic cooldown timer. Make it so there's a 30 second delay or something after you call in the arty, but you can call in as many consecutive missions and types as you have available. Much greater choice, would make for interesting battles, and would be more realistic.