I was very meticulous (maybe too much) in purchasing a burner phone for the hobby. As others have stated that a google voice or other extra numbers through apps on your public facing phone may be easily discovered for anyone who wants to look (SO especially)
1. Probably super obvious... pay everything with cash or visa gift cards purchased with cash: phone and plan cards. No paper trail. Also wear a face mask, hat and baggy clothing when purchasing items (I'm very paranoid)
2. Because of my cash/vgc rule, I went with tracfone as you can still purchase the phone and cards seperately with cash.
3. Get a cheap burner smart phone. Why? Some PO send stuff that requires internet access and flip phones are a pain-in-the-ass to use in a pinch. A smart phone can also be used to set up a burner email and conduct hobby research.
4. Doing everything with cash adds extra hurdles moving forward, don't forget to keep the phone active. I've had to rescreen once when I forgot to reup the phone plan and had to get a new number.
5. Burner phones are most likely android, so don't use a gmail account with your phone (they track everything). It's not required.
6. Again probably super obvious, don't text or call your burner phone with your public one
Some fine folks have already said, but turn off the phone before returning home. In fact don't use it there at all! Despite all these conditions I'm well aware that no privacy or security measures are perfect, but I feel comfortable with the level that I achieved with this method.