Not the most helpful of comments previously but does make some valid points. By the sounds of it you might be embarking on a highly iterative process. My advice would be to buy some RFID wristbands, test them with your readers, break them open and observe what others have done and how they ahve designed their wristband for each level of performance. You'll soon get a feel for it and it is the best way to learn rather than be told what to do. You'll understand the fundamentals that way/
If you are using 13.56Mhz I would go for PCB antenna (FR4) and work from there, but go with above route first.
Word of caution - 10 cm is a litte ambitious for HF.
Also keep an eye on the actual application i.e. what your end game is. You product will need to be robust enough and operate within its intended environement.
Good luck - sounds like fun.