The simplest and easiest type of business for a private practitioner is a sole proprietorship. In fact, you don't even have to file any legal paperwork to establish a sole proprietorship unless the business will operate under its own name rather than yours. There are no ongoing fees to maintain this kind of business, and taxes are relatively straight-forward, since business income is reported on the owner's personal tax return. (This is supposedly beneficial, since otherwise profits would be taxed twice: once as the business's income, and once as income paid to the owner by the business. However, you do also have to remember to pay Social Security and Medicare taxes on your business income).
The downside is that the owner becomes personally liable for business debt (e.g., if you fail to pay bills, collectors can go after your personal accounts and assets). There can also only ever be one owner; adding additional owners would lead to a change in business structure.
If you have or add another owner to the business, whether that person is a spouse/family member or another provider, the next simplest business structure is a partnership. General partnerships are established via a formal or informal partnership agreement. This agreement specifies division of contributions, responsibilities, profits and losses. There are no requirements for this division, as long as their is a business rationale. Each partner reports their share of profits and losses on their personal income taxes - the business is not a separate tax entity. Each partner also retains personal liability for business debts; in fact, creditors can hold a single partner (or each partner) liable for the entirety of the debt.
(There is also something called a limited partnership; however, I don't think that a private practice would ever function as a limited partnership. Limited partnerships have two kinds of partners: general partners who operate the business and are liable for its losses, and limited partners whose only role is to contribute capital and determine who will run the business. Limited partners share in profits, but are only liable for losses to the extent of their contributions. There is more legal paperwork required for this type of partnership).
Some clinicians opt for another form of business: a limited liability company (LLC). LLCs are a hybrid of a partnership and a corporation: like a partnership, the LLC does not pay separate income taxes, and like a corporation, owners are not personally liable for business debt/losses. However, there are significantly more administrative requirements and costs for an LLC compared to a sole proprietorship or partnership. Paperwork has to be filed with the State, and some States may not allow LLCs with only one owner. I live in Massachusetts, and it seems like a single owner is permissible here. However, a form has to be filed with the state at start-up and annually thereafter, with a cost of $500 each time.
It's also important to know that "limited liability" means that no one can come after your personal assets due to business debts...BUT malpractice suits are not business debts. Some practitioners decide on this business structure thinking it will protect their personal assets in case of such a suit. However, both the business and the practitioner as an individual would be named in any suit, and laws governing LLCs specify that liability is not limited in the case of unethical conduct. Given that there is relatively low overhead for a therapy practice, and one would therefore assume limited potential for unpaid debts to add up, limited liability does not seem like a sufficient reason to choose an LLC, at least from my perspective!
Corporations get even more complicated. To form a corporation, articles of incorporation have to be filed with the State (along with money, of course). Corporations have shareholders, directors and officers. There have to be annual meetings, stock certificates to share holders, meeting minutes, and elections. The corporation has to have its own bank accounts and pays separate taxes (meaning income is taxed twice, because each individual's income from the business is also included on personal tax returns. Some earnings can be maintained by the corporation for future expenses and not paid to owners/employees, hwoever, and that income would only be taxed once). The only real benefit beyond the limited liability (which is the same as an LLC) is that corporations can provide fully-deductible fringe benefits (e.g., health insurance, pensions, etc.)
Some alternatives exist to the standard corporation. Close corporations are simplified versions of a corporation for small businesses, and differ State to State. S corporations are also somewhat simpler in that there can be only one owner, and income passes through to the shareholder(s) rather than being taxed separately (and therefore twice). However, fringe benefits may be taxable, there are limits on the maximum number of shareholders, and differences in how capital gains are handled. All of this seems pretty complicated, and unnecessary for a private practice...but that's just my opinion.
I think the sole proprietorship and partnership models seem best suited for private therapy practices. These models also have the advantage that they are easy to dissolve, and practitioners can decide to opt for a more complex structure instead if that makes sense some time in the future. However, I am very much a novice when it comes to this business stuff, so I'd love to hear from others on how you have (or would) set up your business!