First, some back matter might be helpful to you. At the outset, there is no such thing as a healthcare delivery "system" in the US. The term is used because there isn't really another term but it is used euphemistically. Since the inception of Medicare in 1964 and Medicaid in 1968, the direction of healthcare delivery in the US has pivoted on the "managed care organization". The MCO model really came to the forefront in the 1980s when Americans became truly sick of runaway medical costs and demanded a legislative solution to the problem. It is meant to streamline the provision of medical care and to provide it at a lower cost. Whether it actually does so is debatable.
What this means to you as a healthcare consumer is that there is one "gatekeeper" and that is generally the doctor identified as your PCP. He or she is in overall charge of the direction of your healthcare. The gatekeeper system has largely brought an end to the practice of general medicine or family practices, although they can still be found. In my case, my PCP is an internist and I see him four times a year. His sole purpose in life is to refer me to EVERY other specialist in town. When I see him, he checks my height, weight, BP, does a limited exam and checks my pedal pulse. He does draw blood and he has the capability to do x-rays. He gives me my flu vaccine every fall and that's about it.
When I developed a UTI earlier this year, he referred me to a urologist. When I had trouble with trigger finger in both hands, I was sent to an orthopedic surgeon that specializes in hands and upper extremities. Although my PCP can perform a Pap smear, he referred me to a gynecologist. When I developed a pressure ulcer on my leg, I was referred back to the surgical practice that did the original amputation five years ago. In other words, although I'm sure he's a skilled physician, he just doesn't do all that much in the way of actual doctoring, he writes my prescriptions and refers me elsewhere.
As for your original question, the other posters have made good suggestions about how to find a PCP. If you live near a hospital that you would like to use, I would go through their physician directory service, you'll get doctors that can practice at the hospital of your choice. It's quite likely that you won't see your PCP more than once a year, any other care you need will be provided by specialists. Double check the requirements of your insurance coverage and make sure that you're not in an HMO or PPO, they can restrict the doctors you see to those that are in their network.
Good luck in your search.