I've shot all three. In my humble opinion:
Love woodies, but don't have the time nor the tools for proper tuning.
Aluminums may be the best choice for target/3D but your probably going to shoot 1916's or 2016's with 100-145 gr. heads. I was never impressed with penetration of arrows in the 400 grain total weight range. I killed deer with them, but pass throughs weren't frequent, even with well tuned arrows and good shot placement.
Carbons are my choice for lower poundage, even though they can be the most frustrating to tune. .500 spine or weaker, leave them longer than you'd ever think you'd need, and trim very small increments. With 200-250 grains up front, my arrows will weigh 525-550 and pass throughs are expected, even with low-profile 3-blade heads. (and I'm still shooting the first carbons I ever bought, just wish I had a dollar for every fletch I've put on them)