How should a new professor speak to prospective PhD Students? I am a new professor, now interviewing PhD students. I lack many of the things they expect: other PhD students to talk to, a clear narrative about my lab's work (as funding is still in flux), and an academic backstory beyond graduate school. How should I help good students to take a chance on me as an advisor?
It would probably serve you well to find a local experienced mentor to work with and learn from. They can help you with what to say, but they can also help you get the skills you now know you lack. They might even serve as a sort of backup for you in working with students over time. Having a more experienced and well-established member on a student's committee from the start can be a big help to everyone. 

If the work of the lab permits, it is also probably best to start small. Not too many students and work hard to promote their work so that they will promote you in the future. 

But for a more direct answer to the question, I assume that you have established an idea driven research trajectory that you believe has a future. Talk to them about that. Hopefully you are enthusiastic about it, but also have already had some success, if only during your doctoral studies. Try to express your own enthusiasm and what you see as the goals and that you have some ideas about how to achieve them. 

They are taking a risk, of course, if you don't have a track record. You need to work, over time so that any risk of failure is mitigated.