Which style should I start with?
Hatha and yin are usually slower and easier to start with; vinyasa and power are faster and harder. Say what you are looking for rather than picking a style name, and let the instructor advise.
I am not flexible. Is that a problem?
It is the most common reason people give for not starting, and it is backwards: flexibility is an outcome rather than a prerequisite. Say it in your request and you will be pointed at the right class.
Are private sessions worth it?
For an injury, a specific goal, or if a room full of people puts you off, often yes. A few private sessions before joining a class is a common and sensible path.
Can someone come to our workplace?
Many instructors run workplace sessions, usually as a weekly block rather than one-off. Say how many people and how often, since that is what it is priced on.