Cost of studying neurology?

Lots..Staggeringly. First, 4 years of college, then 4 years of medical school...Then a year of internship and then about 3-5 years of residency/fellowship. It takes a lot of money and time and dedication...I am pleased that you are interested, but go talk to a neurologist first before you make a decision...
Your money and life. It will cost you many years but pay great dividends. First through college, then 4 years of medical school, then 1 year of internship then 2 or 3 more years of neurology residency. Additional specialization is available in many fields including critical care, pain medicine, sleep medicine, movement disorders, etc. If you are talented and motivated there is always a way to pay for it.
You have ambitions. Neurology can be a fascinating field and can provide great intellectual stimulation, but takes many years to get trained, and you will find these days an emphasis on subspecializing in various areas of neurological disease, which may require a fellowship. Need to know that med'care and m'aide do not fully value the neurologist's contribution for some bizarre analysis, so there may be challenges.