All good questions. If you just graduated with your BSN, sitting down and setting up some milestones for the next ten years is important. I assume you are not an RN to BSN and that you have no nursing experience? If so, you need at least 2 years nursing experience as a floor RN. Then I would start training for charge nurse positions, or assistant unit managers, house supervisors, etc. Learn as much as you can. If you want a hospital administrator position, like a director or CNO, you have to work your way up the ranks. This almost always involves a unit manager position to start. If you do that for 4-5 years, and have a handle about how it is run 1 unit, start applying for director jobs and manage multiple units for at least 4-5 years. Then I would apply for CNO positions. In the meanwhile, I would get your MSN or MHA (masters of health administration). I think the MBA is less important these days for nurses (this is my opinion). Employers want to see that you can manage a large number of FTE's, stay under budget, have a healthy operating margin, and maintain your quality metrics. You will need a master's in nursing though. Some magnet facilities are requiring that a masters degree for unit managers as entry level and I wouldn't be surprised if that trend increases.
I'm sure managerial director roles exist in medical staffing agencies but I imagine you would have to work up through the ranks there as well. I'm not as familiar with those organizations.
Good luck in your journey! The world is your oyster!