I want to found a company.  And after which I want to be able to give
equity to new team members and stock options to employees and
partners.

How should I start my company if I want to do this?  Afterwards, what
do I need to do to give equity or stock options to someone else?

If it matters, it's an Internet company, and I will be based in China,
though I'm a US citizen and well be targeting users in western
countries.