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/