Psychiatry is becoming more competitive as more US grads enter the field but it still among the least competitive specialities. Rightly or wrongly, if you are a US grad with a decent record you will be seen by many programs to be a more attractive candidate than an IMG.
Like most specialities, the demand for psychiatrists varies from region to region. Some areas of the country desperately need more psychiatrists and if you choose to practice in those areas you will likely have a good practice. Of course, you will probably never make as much as an orthopedic surgeon, etc.
As for career options, there are many. There is, of course, private practice. Psychiatrists can work at a county mental health center, and many younger doctors do a combination of these two options while setting up a practice. You can work at a state mental hospital; the doctors who have done this that I know enjoyed this option because they could work with patients for a longer period of time than in other hospital settings and they don't have to deal with the paperwork, etc., of private practice. You can work in academics, teach, and do research. One area that many doctors are needed in in my area are psychiatrists to do consultations in private hospitals. Then there are the subspecialities of psychiatry -- forensic (where you work to evaluate defendents on their competency to stand trial and their mental state at the time of the alleged events), child, addiction, sleep medicine, etc.
Hope this gives you a little bit of the info you are looking for. I'm sure that others who post here will have more to add. Good luck!