What bandwidth oscilloscope is sufficient for a first time electronic hobbyist looking to just see what this device can do.

 

Welcome to AAC!
That is a difficult question to answer.
If you don't know what the device can do then you don't need it.

 

What bandwidth oscilloscope is sufficient for a first time electronic hobbyist looking to just see what this device can do.

That's impossible to answer without knowing what sort of circuits you intend to build and/or test.

 

What is "this device"?
My crystal ball is out for cleaning.

 

The bandwidth of a scope is the frequency at which the displayed deflected voltage is at 50% the applied value due to frequency limitations of the scope.
e.g if a 100MHz scope was fed a 100MHz sine-wave at 10V peak to peak, the scope would display this as 5V peak to peak.

As a general rule of thumb, you should avoid using a scope at frequencies above 1/10 of its bandwidth to avoid measurement/display errors.
Remember that square waves have high frequency harmonic content, so you need to consider the rise time response of the scope.

These days you can by a small screen 1MHz scope for less than £35.

Note from the specification, although it has a claimed bandwidth of 1MHz, it has a sampling rate of 5MS/s. So in theory a 1MHz sine-wave would display at 50% and the complete sine-wave would be made-up from 5 sample points.

https://www.ebay.co.uk/itm/DSO188-H...454944&hash=item1f0f1949fd:g:hYkAAOSwyhVcrfcL

I’m not recommending you buy the ebay product – it is likely to be poor quality and very difficult to operate given the lack of controls.

 

The bandwidth of a scope is the frequency at which the displayed deflected voltage is at 50% the applied value due to frequency limitations of the scope.
e.g if a 100MHz scope was fed a 100MHz sine-wave at 10V peak to peak, the scope would display this as 5V peak to peak.

As a general rule of thumb, you should avoid using a scope at frequencies above 1/10 of its bandwidth to avoid measurement/display errors.
Remember that square waves have high frequency harmonic content, so you need to consider the rise time response of the scope.

These days you can by a small screen 1MHz scope for less than £35.

Note from the specification, although it has a claimed bandwidth of 1MHz, it has a sampling rate of 5MS/s. So in theory a 1MHz sine-wave would display at 50% and the complete sine-wave would be made-up from 5 sample points.

https://www.ebay.co.uk/itm/DSO188-H...454944&hash=item1f0f1949fd:g:hYkAAOSwyhVcrfcL

I’m not recommending you buy the ebay product – it is likely to be poor quality and very difficult to operate given the lack of controls.

That's not entirely correct.
Scope BW is measured to where a 'leveled' sinewave is no more than 3dB down from its max value.
Eg, 1V p-p sinewave measures 0.707V, which at that frequency measurement determines the scopes BW.

A 100 MHz rated DSO will typically return a -3dB point of some 120 MHz.

OP, your immediate scope needs will be where your interest takes you, be it RF, analogue or digital which really are all analogue signals but in different frequency ranges. Typically the benchmark for general use today is 100 MHz where a decade or 2 ago this was the realms of expensive gear where that is not the case today. Generally those that dive headlong into electronics regret not spending a little more on their first scope so to have additional features and be able to grow into this capability.
More important to you is the budget available and if you are prepared to invest in equipment that will serve you well while your skills and knowledge grow.

 

In addition to what @tautech mentioned above, keep in mind that a square wave of a given frequency requires much more bandwidth than a sinusoidal wave of the same frequency - roughly 5 times more bandwidth, although 9 times more will give you a more faithful representation of the wave.

https://www.allaboutcircuits.com/textbook/alternating-current/chpt-7/square-wave-signals/

In practice that means that a typical 100MHz oscilloscope can show a nice square wave of 10~20MHz. Above that and distortions may start to fool you into thinking the circuit is defective or operating in a weird way.

Square waves are found in digital circuits everywhere, thus is an important consideration to better define the type of equipment you need.

 

You can get a $15 200kHz mini-scope on any place like ebay/amazon/etc, that for the price, can show you all kinds of stuff, including all kinds of audio.

I think they are cool. Even a professional EE could do a lot more with 1 of them, than with just a DMM. I'd recommend 1 with a case, or make 1 yourself. Mine had a plastic case, but it was cut wrong, and didn't fit together. That reminds me, I should fix that with my new tools.

I have 3-4 working scopes, but I'd still use 1 of these just for fun on some circuits. I should use all my scopes once and a while, they will get lonely otherwise.