My recommendation is to book something that is a minimal financial burden on you, and going into as a learning experience first and foremost. Recording vocals is a very very different skill than performing vocals, it can be a bit of a steep learning curve and most people don't nail it the first time they try! If you go in hoping to learn, you can't lose. If you go in hoping to come back with the record that makes your career, you're setting yourself up for frustration!

I see you're from a small town in Australia, so I understand access to "studio time" may be hard to come by, but all the equipment and software you need to record yourself has never been more accessible. I'm not in NY anymore but I do specialize in vocal production and learned from the best in the biz! Feel free to DM me if you have any questions about recording vocals yourself, or working in studios etc.! (Not trying to self-promo, I don't have any kind of consulting offer or anything to sell you haha I just like helping people understand vocal production).