'Tidy' is understandable in AE, but probably not the first choice. To me it sounds a bit old-fashioned.
I would say 'neat.' Her room and school things are always neat, in order, kept straight, picked up. She's a neat, orderly, organized, disciplined person. She's not messy, her room and things are never messy.
'Neat' can also be just a general positive adjective, like cool, great, super, interesting, nice, etc. So if you just say she's a neat person without further context, it could be ambiguous; it might just mean you really like or admire her.
I would use meticulous or thorough more for written work, checking the details, not overlooking anything.