If you have a decent reliable computer I would suggest getting an audio interface and a mic. The interface will allow you to record to a computer. From there you can record, edit, mix, etc. The thing to consider would be how many inputs will he use at one time. If it will just be him recording himself, or just one instrument at a time you can go with a small simple interface with only one or two inputs. If he eventually wants to get into more multitrack recording then he'll need more inputs. Many interfaces come with their own software so you wouldn't have an added expense there. As far as which you should get, it's all subjective. I have an
Mbox 2 mini which would work well for you if you don't need more inputs. It comes with ProTools as well, which is a plus (depending on how you look at it). The downside is the price. There are far more interfaces out there a lot cheaper that will do the same thing. There is no sense spending a lot of money when he's just starting out.
Another option would be download "audacity" recording software (free) and get a USB mic. This will probably be your cheapest option, but with that comes cheaper results. For just starting out, and being on a budget, this may be the way to go.
Those are probably your cheapest options. Next you could look into stand alone digital mixing consoles. There are a lot now that have their own hard drives and burners in them. These will probably be a little too big and pricey for him.
After that you would need a mic. I haven't done a lot of brass of woodwind recording so I'm not sure what would be best for those recordings. My suggestion would be something like an
SM57. It can record anything you put in front of it, and if your son wants to keep recording its always good to have some 57s in the closet. Like interfaces, there are tons of mics to choose from, and everyone will have their own opinions of whats better. If he wants to record a group it may pay off to get a stereo pair of condenser mics to get a good stereo recording of something like a quartet.
I would search some of the online retailers for audio interfaces and getting some info about them. From there you can get an idea of whats there and the prices. Also look at used stores in your area, pawnshops and craigslist. Places like that can save you good chunks of money.