I have been looking for a simple oscilloscope for my 14 year old's birthday coming next week.
All tools have a learning curve. A beginner benefits from a short learning curve, which implies a simple tool without too many config variables.
Analogue scopes are simpler than digitising scopes. There are fewer things to tweak, and everything is visible on the front panel (not buried in some menuing system).
I would consider getting a
cheap and
working analogue scope, for about £1/MHz. Yes, he will probably outgrow it, eventually, but by then he will know what he
needs in the next scope.
A 20MHz analogue scope will be fine for audio and mechatronic circuits, and will be adequate for digital circuits. (Avoid analogue storage scopes like the plague!)
If you want to capture one-off transients (e.g. a PSU startup) then a digitising scope is necessary. But it is often possible to make whatever you are looking at repetitive, in which case an analogue scope is sufficient.
Don't forget to include the cost of probes.
Don't forget that a scope chassis and therefore the probes' screen must be directly connected to earth. Touch that to the wrong point and there will be noises and smells in the air
Consider buying a simple bench PSU, to isolate the UUT from the mains.
If you can get an educational discount, then consider the Digilent Analogue Discovery. It is surprisingly capable, and includes other useful instruments (function generator, pattern generator, logic analyser). It is
not suitable for general purpose use with high voltages, but is great for anything up to, say, +-20V.