I started on horn in 6th grade (earliest school band is offered where I grew up). We were able to borrow one from a family friend that wasn't using one and then bought it after a year. I wanted to play trumpet like the cool kids, but the horn was free and my mother made me play horn to start. I quickly decided that being the only horn player was better than being one of 10 trumpet players. I was always first chair, haha.
But then I also found I was quite good at it, which helps. It paid for college - music degree - and then some. If I hadn't have screwed up my left shoulder not long after college I'd have kept trying to play professionally.
I would rent to start, perhaps. As has been said, maintenance on a horn isn't cheap, but it isn't outrageous compared to other instruments - they all have their own quirks.
While I can understand the teacher wanting him to start on a single horn, I would not stay on a single more than a year or two and would get into a double as soon as he thinks he might want to stick with it. It's like driving a manual vs. stick shift - it's a car, but very different. A double horn is superior in all ways, but a single is ok to start when young - it is lighter and only one set of fingerings to learn. High notes are more difficult on a single, however, especially for an inexperienced player.
The only brands you didn't mention in your initial list are Holton and Conn.
As for age, the best horns, to many, were made in the 1950s. All those movie soundtracks you hear with the soaring horn lines that are so amazing? Almost all of those studio guys in LA are playing on Conn 8D horns built in the 50s. You want one in good shape, of course. Finding one of those will also run you a minimum of $4-5,000, probably more. A high end concert horn from one of the best makers will be in the $8-10,000 range. I've seen them over $12,000.
If you have questions or need advice or opinions on a horn or playing feel free to PM me. Always happy to help a young player get started.
And while the horn is the most difficult of all instruments to play well, it is also the most special, the instrument of God. When movies want something really inspirational? Horns. When they want poigniant? Horns. Romantic? Horns. Angry? Horns. Jacks of all trades in the music world, we are.
ETA: I would add that trumpet embrouchure is completely opposite of horn and at no time should he play both instruments if he is serious about either unless he is a freak of nature that can switch back and forth without impairing either (I've only known one or two who fit that description in my life). Trombone/euphonium/baritone, on the other hand, have similar embrouchures - though a much larger mouthpiece - and I never had trouble switching between those. I spent multiple years in late high school and college playing trombone or euphonium in 2nd band or brass ensembles to help fill out sections (play horn in band 1, trombone in band 2 - you just can't play the same instrument in both, etc).
