By home-care business, its not clear whether you mean hospice care, non-medical home care, child day care, or something else. Each one involves its own licensing and regulations which vary state-by-state. Plus, as you're starting this on your own, you need to factor in what happens if you're sick or can't meet your appointments -- in other words, home-care is a very team-intensive business and requires the help of others to run well (in some ways more so than other kinds of businesses).
The best way to start is to go through one of the many books available on "how to start a . . ." business. They will give you the run-down of what you need to know and where you should look including goverment agencies, other websites, resources, etc. Speak to an attorney and accountant who have worked with businesses of this type, as they may require special clearance from the state Department of Health or Department of Education, depending on what you're intending to do. Your advisors will also help you protect you by forming a business entity, making sure you have the right insurance in place, and getting you properly licesned. But do the initial information-gathering yourself so that you have some familiarity with the process, steps, and costs involved.