the short answer
Most coaches start as a sole proprietor because it is the default and costs nothing to begin. Many later form an LLC to separate business liability from personal assets, and a smaller number elect S-corp status once profit is high enough to justify payroll and extra filings. A personal trainer LLC is mainly a liability decision, not a magic tax cut - and none of it replaces insurance, a signed client agreement, or advice from a professional in your own country.
A note before you read: this article is general information for coaches, not legal, tax, or financial advice. Business structures, their names, costs, and tax treatment vary by country and state and change over time, so treat everything here as a starting point for a conversation with a qualified accountant or attorney. It also sits inside your scope as a coach - you advise on training and nutrition, never on a client's legal, tax, or medical situation.