When you do your psychiatry and neurology clerkships you can decide which you want to do. There are three routes to what you call 'neuropsychiatry'. One is to do a combined 6-year neurology/psychiatry residency (the first year is mainly internal medicine followed by 2.5 years of post-internship training in both neurology and psychiatry). This route is best for those who are interested in both neurology and psychiatry, and not just cognitive neuroscience or behavioral neurology but everything - peripheral nervous system disorders, epilepsy, stroke, headache, movement disorders and so on. You will not get very good psychotherapy training, which is fairly important in neuropsychiatry depending on what you want to do, and there is some really interesting research on the neural basis of psychotherapy. These have largely fallen out of favor for various reasons (most neurologists dont like psychiatry, most psychiatry wannabes dont like neurology, it is 6 years, they are keen on neuroscience PhDs, it is not clear what the job opportunities are, it is clearly the biomedical approach to psychiatry is not the future, there has been an upswing in psychotherapy etc). These programs frequently go unfilled.
If you are predominatly interested in training in neurology you can do a 4-year neurology residency followed by a 1-2 year cognitive neurology or behavioral neurology fellowship. This is not a ACGME approved fellowship, and it is not a recognised subspecialty by the American Board of Neurology and Psychiatry. A major part of this is dementias, neurodegenerative disease, and cognitive and behavioral aspects of stroke, traumatic brain injury, epilepsy, movement disorders etc.
The 3rd pathway is to do a 4 year psychiatry residency followed by a 1-2 year fellowship in neuropsychiatry or behavioral neurology. If you are primarily interested in the mind, and emotional, cognitive and behavioral dysfunction from a cognitive neuroscience perspective then this is the way to go. You will become proficient in diagnosis and management of common mental disorders (schizophrenia, bipolar, depression, PTSD, personality disorders), au fait with psychopharmacology, psychodynamic therapy, cognitive behavior therapy, and supportive psychotherapy, and ECT. This route will be good for dealing with conversion disorders, depersonalization, cognitive deficits in psychiatric illness, dementia, traumatic brain injury, psychiatric aspects of epilepsy, Tourette's syndrome, Parkinson's disease etc.
Neuropsychiatry is a predominantly academic field and most are based in academic centers with faculty positions, often doing research. Many are MD PhDs (but this is not necessary, and you do not have to research necessarily). It is a niche area and hard but possible to carve out a private practice (and doing so would usually require a strong academic reputation).
As for where to go for medical school- well go to the best school you can without bankrupting yourself. Neurology, psychiatry, and neuropsychiatry are ridiculously uncompetitive fields (except at the top top programs) you will be fine. It is too early for you to know what you really want to do, but it would be useful to go somewhere that could support your interests in this area (so you could do research etc) but certainly not necessary. Harvard and Hopkins spring to mind, and I think NYU, Brown, Dartmouth and UCSF are also strong here.