Ya, there’s nothing like face-to-face lessons. Some books have really good illustrations and some folks are a bit more patient than others for this way of learning. I started out on my own for a year or so and when I found a good teacher he had to help me break a bad habit or two and then I was away.
As far as mouthpieces go, no, they are not interchangeable! They differ in size just like the horns themselves. For alto you can’t go wrong starting with a Meyer, Selmer S80, or Yamaha…I have some mouthpiece reviews you can find on the right side menu for more info.
cheers
Johnny

Good one Howard, 30 seconds wow!
Long tones like you suggest are one of the best things we can do to improve our tone.
But again, if you’re doing something wrong like breathing or embouchure you won’t be quite there yet
and you may have to break some bad habits, that’s where an experienced teacher can help.