At the very least a dress shirt with tie, dress trousers and dress shoes. Going up from there add a sports coat, one more up dark suit, one more up tuxedo.
Good oppertunity for them to learn comformity to rules, also the girls like to see the boys dressed up.
My son was 15 and 19 when we cruised. He did not have a suit and did not want one. We got him some real nice slacks, shirt and tie. He was happy with that and so where we. Maybe on our next cruise (he's now over 21) we will get him in a suit but back then it was not necessary and I'm sure your sons would agree also.
Golden Princess 12/04
Enchantment of the Seas 4/02