You definitely want a contract in place. Depending on whether you're a full partner (with 33 or 50% equity) vs a contributing member, you may want to use a SAFE or simple agreement for future equity.

Splits in work and responsibility are definitely tough, especially when you're offering a very specific expertise and working part time.

If you're doing this for huge scale with VCs involved, you want to make sure all your ts are crossed (documents, contracts etc). But if you're exploring an idea with friends, the first thing is to validate your hypothesis with an MVP.

I've written a bit about arrangements in early companies for equity and cash here.

https://mvpengineer.com/pros-and-cons-of-equity-based-technical-cofounders/

Hi
Good question.
There are definitely documents between co-founders. The most important one being a 'co-founder' agreement. I draft lots of them each month, and this is a very important agreement (especially considering that the #3 reason for startup failures is fights between co-founders).
You also want to be sure that the stock is allocated to you. This can be done by giving you a A Deed of Assignment of Stock Subscription, or by updating the company registrar of the transfer of stocks (shares) - but the process depends on which state the company is registered in.

Good luck

I am a mentor on Startups.com, an international lecturer on entrepreneurship and negotiation, and a commercial startup lawyer. I've successfully helped over 400 entrepreneurs, startups and businesses and I would be happy to help you. When scheduling a call, please send me some background information and the 2 main questions you want answered so that I can prepare in advance (to give you maximum value for your money). My reviews: https://clarity.fm/assafben-david

Here is a pretty good guide with a lot of examples that will be helpful:

https://startupguide.hbs.edu/people/founding-team/key-terms-to-include-in-a-founders-agreement/

Everything I read in the guide agrees with my own experience from my past two startups.

After reading through that guide, you can look at this more detailed customizable outline of a cofounders agreement, which has various options embedded in it for key decisions.

https://www.law.upenn.edu/clinic/entrepreneurship/startupkit/founders-agreement.pdf

The options in it are ones that you will have a general understanding of from the previous guide.