Realize this: whatever you take with you, and whatever bag you take it in, will end up being held over your head for an indeterminate period, run with, dumped and thrown, along with everything the Army is going to issue you. So save yourself the trouble and travel light.
1. Take a blank check as well as your bank card. The bank card does not have your account info on it, so you won't be able to fill out your direct deposit forms without the info on the face of a check.
2. Your orders, transcripts, etc. will be in a folder that you leave MEPS with. For other critical documents, I recommend scanning them into pdf format and taking copies on a thumb drive. If you run into issues, your DS will be able to get you computer access to print copies. This includes marriage and divorce papers, birth certificates, your contract, lease or mortgage if applicable, etc.
3. Don't bother buying new running shoes before you leave. Your DS will examine your feet and tell you what kind to buy during the first week at the PX. You will be given a "stored value" card with which to make that and other purchases. $250, IIRC.
4. Keep the hygiene kit simple and stick to travel sizes.
5. One small towel should suffice. You will only use it for a couple of days until you get your Army issue towels.
6. You can buy stationary at the PX, but the stamps are a really good idea. Take a full roll - you will use more than 20 and can use the others as currency. Even more importantly, pick up a plastic organizer with internal dividers and an elastic closure. This will help you keep everything organized, including the mail you receive once there.
7. If you buy shower shoes, make sure that they are plain black and have no logos of any kind.
8. Buy yourself a couple of Rite in the Rain pocket notebooks and write your key addresses and phone numbers in the back of one. They are waterproof and will save you some grief. Also, Drill Sergeants like it when people write down what they say (especially if you become a PL).
9. Use a Sharpie to mark every item that you have with you during BCT. Take an extra Sharpie to help your buddies. You are about to witness crazy acts of thievery. I have seen soldier's dirty underwear go missing while they were in the shower.
10. Pick up a red lens Photon Microlight and put it on the chain with your dog tags. It will come in handy and you'll use it much more than the crappy L-shaped lights available in the PX.
11. Gold Bond foot powder. Gold Bond crotch powder. Buy them at the PX.
12. Carry everything in a small book bag or day pack, organized in gallon ziplocs. It will get dumped during shake down and this will make your life easier.
13. If you have a cell phone, take it. It will make life easier on Family Day.