Private schools are not necessarily harder to get into. Search for the Common Data Set for each school to see test score ranges. Their websites will tell you the cost of tuition, room & board, and fees for students who do not live in-state. You also will need to add a couple thousand dollars for health care, travel expenses, and remember that dorms either aren’t open at all or they charge extra over the long winter break.
If you want to go to med school in the US, that is very challenging for international students.