There were 3 things I figured.
1. He's in BCT. I've been through basic. Except for shampoo, toothpaste, deodorant, etc... there isn't that much to really spend money on during those first 5 weeks. Anything that's actually IMPORTANT, will be provided to you.
2. If my son really started running low on discretionary cash, we were sending him letters literally EVERY DAY. If he mentioned needing money, I can slip $20 in a few of the envelopes. "I wouldn't put all my eggs in one basket in case it was lost; e.g. I wouldn't put $100 in cash in one envelope". But I have absolutely no problem sending $20 in cash in an envelope.
3. We live 2 hours from the academy. If my son was still having financial issues come "A-Day" because there's something he really needed; such as a new printer, watch, glasses, etc... and his pay wasn't going to cover it; we'd be seeing him on A-Day. Just give him more money then.
Now; because our daughter got a full ride to college, and saved us a lot of money, my wife and I figured we would give her a monthly allowance in college. This way she wouldn't need to get a part time job for spending money. Least we could do considering college didn't cost us anything. Well, my wife figured our son did the same thing by going to the academy. "She doesn't understand the military is paying him". (Actually she understands, but thinks it's fair to give him money every month for spending. Just like his sister.)
Between my son at the academy and my daughter who graduated college 2 years ago; even at an inexpensive state college, they've saved us over $100,000. We don't mind giving them extra spending money.
But whether you give your kid $100 or $300, realize that it's basically to cover them until they start getting a paycheck. But remember: It's not like they are going to go out and order a pizza or going to the mall. They really don't need that much money.