From what I know of the culture (entering school this fall), you can go to any med school you want and practice any specialty you want, as long as you do well on the boards, get decent grades, and show extracurricular interest in the specialty you want to pursue.
Some specialties are much, much more competitive than others (radiology, dermatology, opthalmology, radiation oncology, surgery, ENT, some internal medicine subspecialties too), and specialties like pediatrics, family practice, psychiatry are not as competitive. Therefore, you need better scores on the board exams (mainly step one) and extracurriculars (research, third year related rotations with letters of recommendation) to get into the more competitive specialties.
DO schools tend to shunt their graduates towards primary care specialties (family med, peds, etc), but DO's can also practice whatever specialty they want as long as they do well on their boards and do everything possible to make themselves competitive applicants to more selective residencies.
Hope that answers some of your questions.