Get paid now. Build a prototype. Test the viability of the product and the business partnership at the same time. If you're excited to double down on it all after initial experiments, then talk about a partnership / equity. (The conversation should start at split equally)

If you make a deal with some small portion of equity now, you set your price too soon. Making it harder to get equal partnership. Better to explore the relationship first with a easy and fair exchange of value (work for $).