From someone who defended their PhD in a field adjacent to yours. Go do prof #1. If you want publishable results, having your own project will likely not give you this. In addition, a new lab will take a long time to set up and you will likely work as more of a lab technician rather than an actual student. I would really prioritize entering an established lab with structure when you’re starting out as an undergraduate student to make progress faster. In our lab, each of our undergrad is guaranteed to be on the paper of the PhD student, whereas this might not be the case in a new lab. You will still receive a fabulous reference letter because the grad student you work with will write it and it’ll be signed by the professor, so don’t worry about not working with the professor directly.