If you’re serious about being a good teacher:
Work towards a certificate. Many states have intern programs for public schools where you can take classes while being hired on a temporary basis. It’s how I got my start. Much of what you will learn in your classes is a waste of time, but as a teacher who’s had 6 student teachers over the years, I can tell you the best ones are the ones who actively seek to apply what they’ve learned or are learning in their education classes.
Understand that subject matter knowledge is important but not THAT important. There’s a joke that goes something like, just make sure to stay one day ahead of the kids. Learning how to effectively communicate the basics of your subject and learning how to guide your students to their own learning is far more important than just cramming information into your student’ heads. When I started with my Anatomy classes, all I wanted to do was lecture like a college professor. I had my MS with a specialization in Cardiac Rehab And thought I was the stuff. Unfortunately I was boring my students to death. Our school used to do this thing where graduating seniors would write something nice about 2 teachers on a survey and then all those comments would be sent out. My first year, I got 1 comment. The English teacher after me in the alphabet had a whole page filled up with nice comments. So, remember, a bunch of that stuff that seems dumb in pedagogy classes is actually pretty useful in getting kids to engage in the subject matter.
Sounds like you’d want to teach bio. Pick up a chem credential as well. I’ve interviewed for new teachers 4 times as department chair. The two times we’ve hired chem teachers, we interviewed exactly one candidate each time. When we interviewed for bio, we interviewed 7-8 good candidates and plenty more didn’t make it through the paper screening. You probably know enough chem to take the state exam where you live, so do that.
Understand that being a good teacher is tough. I feel like I’m pretty good at my job. Last year I was nominated for our regional teacher of the year award, but lost to a guy that gave a funny speech while I played it straight. But, it took a long time for me to get good. Many teachers fail to improve after the first year or two. Don’t be one of them.
Public, private, it doesn’t matter. Kids, for the most part, are kids and each scenario will present it’s own challenges.