M.6.
I just had 2 kids go through basic (one is actually still there) - one Army and one Air Force.
They really cannot bring anything at all. $50 is the max they can arrive with (and they don't need money anyways, as they are issued an Eagle Card with funds advanced from their pay) so I wouldn't do money. Stamps, envelopes, paper are all ok. We also gave our son a religious medallion that he could wear around his neck (Soldier of God). However, that may be too personal - I don't know his faith or how close you are to this kid. They can also bring a bible.
The biggest gift you can give to ANY kid in basic is the gift of letter writing. Get his address from the parents as soon as they have it (usually in about 10 days after he leaves processing) and start writing. Seriously, they cannot have too many letters!!! They have to do push ups for them, but they don't care - I swear. When you send letters, use only white envelopes, no markings or stickers on the outside, no extra writing, must have return address or it will be destroyed. Write in the letter that he does not have to write back - they are exhausted. Include an extra strip of stamps occasionally in your letters - they are like gold at Basic. Write positive, uplifting, messages. Funny jokes are great. Silly anagrams of his name. If you want, do a little questionnaire that he can just fill in the blank like "my drill sgt yells more than _________", "my favorite thing to eat here is __________" and include a return SASE with it so all he has to do is fill in a few blanks and put it in the envelope you provide.
Please thank him for serving our great country!!!