Beginning players should all have access to an instrument that is tight, free of dents, decent valves, and mainline manufacture. The mouthpiece needs to be matched to the student, not vice versa. There is no single mouthpiece for all beginners!
Teachers and band directors should have a full complement of mouthpiece sizes from small to large for the student to be evaluated on.

Producing a single tone with the instructor on a selection of mouthpieces takes a little more time, but will lead to a much better experience.

A short lesson on cleaning and care, and of course a decent case will protect the horn. The concept of the "step up" horn is foreign to me. There is the beginning student model and then a pro model. Yes there is a top level of custom horns, but they are a class by themselves.

By the time a student is 14 or 15 years old they should have an instrument that could last them a lifetime.

Not all foreign manufacturers are equal. es there are some horns from China that play well. But be careful! I do not want to get into recommendations here, but I will add that even a Monette can be purchased on ebay.

As far as price goes I like the beginner to have a new student model from $500 - $800. I think the next horn should be purchased with the guidance of a teacher, and many older top line horns are available from $800 - $1500.

All levels of players should expect to pay between $45 and $125 for a mouthpiece.

On a recent scavanging trip to music stores, I picked up several top line two piece mouthpieces at one tenth the advertised price!