Your equity arrangements as well as many other important factors will evolve by developing a business plan and an operating agreement as a team prior to registering the company and its owners with your government or adding your prospective partner as an owner.
In short, develop a vision together of the company and its operations and agree on your respective roles it it. The ownership shares should be a fallout of that process to be meaningful, realistic and successful.
Then develop an operating agreement. It should be a simple, straightforward document you and your prospective partner can draft yourselves, addressing such matters as % of ownership, how revenue will be distributed and other general matters, as well as who can commit the company in the form of credit cards, who signs checks on the company account and other administrative matters. Buying out a partner should also be covered.
I have seen many enterprises fail or go through terrifically hard times due to lack of an operating agreement. The parties should sign it after a review by a lawyer. It should then be notarized and made an official part of the company file.