A few opinions below:
You’ll find out about the schools/teachers/programs over the next year and a half. It’s a long process of discovery. You will think that one school is a no go only to find out there is a teacher that would be great for your kid. You’ll think your kid wants to do both…and then in 6 months…they change their mind. Most parents on here will attest to a lot changing over Jr and Sr year.
So…when in doubt, spread it out. Have a variety of schools…even the scary ones with only a few spots. I wouldn’t remove schools until later when it’s very obvious it’s a no.
How to make the list: keep asking people for information. His private and school teachers should be helpful. This site can be helpful along with other places. Maybe he goes to a Sat school? Or participate in some music honors program. Keep asking for information.
Contact music admissions at the school. Remember they can be a bit of the “sales arm” of the dept so you may get the old “sure he can do that”. But you can ask for example: how many kids do both classical and jazz. Could we communicate with a student directly about their experience. This is not an uncommon “ask”.
Parents do differ on who should contact the school. If it’s contact with a teacher (or student), I feel that it should only be the student (your kid). However, for music admissions, I think that it’s fine for a parent to do some of the leg work. I would be blunt with the school about the cost to travel and therefore you trying to some leg work on the program before buying a ticket. Most schools are very understanding about this. You could also get an email address to a key administrator and have your kid send the questions.
Some people worry that if they do approach the school in the wrong way, they could tank their kid’s opportunity. That is not true. I don’t think you’ll see an administrator in the audition room! Of course, be short and concise…and not a pain!
Finally, many moons ago, we did none of this. We stumbled around, wasted money, were confused often….and my D still got acceptances. She even started at her school…and we all thought she’d have lots of flexibility. Many students start as double degrees etc…and then reality sets in about the work load…and everything starts to narrow a bit. That’s OK in the end. Just be sure that it is a stimulating environment. People can overlook all the extracurricular, student produced activities. In some cases, that is where students can get outside their core studies and find enrichment in other areas of music. Another thing to ask about…
Good luck!