There are several different kinds of liability insurance you are likely going to need, and you might need to obtain them from different sources. Your everyday General Liability coverage which will provide premises liability can be obtained from most any insurance agent/broker that handles business insurance.
But as a health care provider, you are also likely going to need professional liability insurance--that is, errors & omissions coverage, AKA malpractice insurance. This is a more specialized coverage, and you should likely check a couple different sources. You might want to check your local medical association, as many offer professional liability coverage to members. You should also contact a specialist broker that handles professional liability--an internet search should provide several sources.
Finally, depending upon the particular state you are in, you are likely to need Workers Compensation insurance. Even though you say most of your workers will be independent contractors, in most states this does not absolve you of your liability for Workers Compensation. In most (but not all) states, any employer that utilizes the services of an uninsured independent contractor is responsible for Workers Compensation for such contractors. So you will again need to be talking with your local insurance agent/broker that handles business insurance. A few states require you to obtain Workers Comp coverage from their state fund (currently Ohio, Wyoming, Puerto Rico, U.S. Virgin Islands, and Washington use these monopoly state funds.)
Some other states use state funds that compete with private insurance companies--California, Colorado, Idaho, Maryland, Montana, New York, Oklahoma, Oregon, Pennsylvania, and Utah. All other states require you to obtain an insurance policy form an approved insurance company (unless your company is large enough to be approved to self-insure. Generally, you have to be fairly large, though.)
In those states that don't have state funds, there is a mechanism called Assigned Risk Plan, where companies can get WC coverage even when insurance companies aren't interested in voluntarily writing the insurance. Most smaller employers end up in Assigned Risk plans by default, as insurers are usually only interested in writing companies that generate larger premiums--but there are exceptions to this, so check around. Assigned Risk coverage in most states is a lot more expensive than what you can get in the voluntary market, so it can pay to shop around and get voluntary market coverage if at all possible. Check with multiple insurance agents, too, as different agents have access to different insurance companies.
