I'm not saying that he shouldn't be curious and play with batteries , arduinos , dc motors, ...ect (I did that when I was his age , I'm 25 so not that long ago) , but at his age he is not going to understand how to properly measure different voltages (specialy with a scope) or for that matter what a waveform on screen actually represent.
I understand that some of the older members on this forum , started by playing with tube equipment and I respect that , but electronics has advanced quite a bit from that. These days most of the stuff is in discrete packages or in SMD form. Not really meant to be repaired.
If he buys himselfe a scope , for him it's most likely going to be a fancy toy , so I'm just trying to tell him that at his age he should really be focusing on his school.
I know that is boring but companies these days are not really looking for guys with great soldering skills or guys that build circuits in their garage (they have Chinese for that ). If he wishes to make electronics his career , he is gonna have to do it the hard way , by getting college degree.
I think you should think it backwards. If he starts playing with a $10 scope now, like what he's planning, and even better, if he puts something together by himself, by the time he has your age (or mine FWIW, I'm 28) he will dominate scopes if he keeps at this. He's planning to use an arduino to capture some data, and display it somehow, add some attenuator at the input, if you want, call it a scope.
And no, when I was his age µC were already a thing and tubes already were museum pieces, but as I'm a guitar player with 15yo I built a tube amp for my self with the help of a friend, and right after finishing it disassembled completely and assembled it again with some mods but this time alone.
Coming back to "you have to think it backwards", if he starts soldering components and building simple stuff now, and getting things to work by intuition, he will develop a skill that's very hard to develop the other way around, and that's the feel of a ball park, eye ball, rule of thumb or what you wanna call it. Takes a lot of experience to get that, and once you are in the university you put all your time in theory, for the time you finish you have to take the calculator out to choose a base resistor for a single transistor amplifier. If you had to do it by guess before learning the theory, and then you learn the theory that gets much easier. That's my experience, and my surrounding fellows who needed to take the calculator out to guess a few polarization resistors to get a single transistor to work.
SMD packages are totally solderable, if he learns to solder now, at you age will make BGAs with a hot knife on the stove. And again we should call Rossmann who's been mentioned here, and in some other topics, you can repair the smallest stuff around, if for the owner it's worth paying a few hundred bux for your work. I charged that for a PCB swap last week, could got more for myself and less for the PCB manufacturer if I repaired the thing but I don't have the tooling, and the costumer would payed less, I desperately need a hot soldering station!
I'm just putting together a pro lab, going to get some gear tomorrow I bought online but it will pay for itself in a few jobs I get, aside for my day job from where I'm taking the money to buy the things.
@Eka: sorry, I messed names...
@Cody: Don't let people take you down on this, it will become an income before you think! And for your situation I know that's a good thing, I'm not telling quit school and put yourself to this but you could be repairing some stuff (like swap TV caps) maybe in a year and get money back in your spare time! Family, neighbors, etc. will be your first costumers. If you are known for knowing electronics you will start getting calls for really simple stuff and people will be more than willing to pay for your time. Someone could call you just to connect his new media center!
JS