Oscilloscopes - what specs to look for?

Small parasitic capacitance (even few pF) is enough to produce noise.  Every scope I've ever used showed small high frequency noise when touching other circuit, even with probe shorted.  It becomes a problem only when you need to look at mV level signals at high frequency, otherwise you can just limit bandwidth of the scope (or use two channels and take a difference).  I agree that truly differential input should help, but even probe itself has slightly different inductance of both wires.  If you don't have this problem - great.  Perhaps you have better scope, I ever used.

Yes, there is alway some antenna, but there is a pronounced increase in noise when shorted probe touches the other circuit (shorted with wire loop or two-pin adapter).
Battery powered scopes also show this to some extend, because of these tiny capacitances. Few pF becomes only few hundred ohm of reactive impedance at 100MHz frequency.

eyrepm, As Eric said 20MHz is an overkill for audio, but I would buy scope for any possible future adventure in electronics. The basic decision is how much you’re willing to pay. You can buy unknown brand for 30% of the established brand. What you’re looking for is around $200 for no name brand like one here:
https://www.amazon.com/Hantek-DSO5072P-Digital-Oscilloscope-Bandwidth/dp/B00RJPXB6Y/ref=sr_1_9?dchild=1&keywords=oscilloscope&qid=1586197467&sr=8-9
or 3x that for known brand like this one:
https://www.amazon.com/KEYSIGHT-EDUX1002A-InfiniiVision-Digital-Oscilloscope/dp/B06WXXBXKZ/ref=sr_1_2?dchild=1&keywords=oscilloscope+keysight&qid=1586197860&sr=8-2

Most of the scopes available now are sampling scopes, meaning they A/D signal. Benefit of that is memory function, while drawback is possible aliasing showing false results. I would go for 2 channel, 1Gs/s (most likely half of that when using both channels), 2mV per division vertical resolution and 5ns per division horizontal resolution. Many scopes have built in additional functions like Multimeter, FFT analyzer, Generator etc. I would go for Keysight and pay $600 because of quality, but Hantek might be OK. There are many things that can go wrong with the scope (mostly switches) so if you go with Hantek - investigate. Keysight used to be Agilent, that used to be Hewlet Packard (wonderful scopes). I used Agilent scopes at work.
On the other hand it is complicated instrument. Are you willing to learn? How much time you can invest? There are $50 toy scopes that might be adequate for basic functions in audio band.

Datasheet (just in case):
https://www.keysight.com/us/en/assets/7018-05520/data-sheets/5992-1965.pdf

My company has Keithley Multimeters that are about 50 years old and all of them work fine (are tested every year). That’s quality. On the other hand I won’t be living that long ;)

Let me know more about your needs/plans.

@jaytor , I noticed that Siglent SDS1202X-E, sold and shipped by Amazon for $359 is identical to LeCroy T3DSO1102 sold for $725.
I read that LeCroy relabels Siglent scopes.  That would suggest that Siglent is a quality brand.  Perhaps one day I will get one for myself.

Ground on a scope is normally chassis ground (on all except fully isolated). Careful when you connect ground both for potential for a short and noise you didn't expect.

Even when scope is fully isolated there will be always some very small capacitance between BNC connector ground and the earth ground.  Because of that, probing any circuit that is not battery powered can deliver nonexistent noise, even if probe is shorted on the probed circuit ground.   It happens because there will be small current between probed circuit ground and scope's ground causing voltage drop on the probe's return.  Scope will "see" this voltage drop as a signal (since input is related to BNC connector GND and not the end of the probe GND).  It is just in case you wonder why scope shows anything (very small HF noise) when you touch circuit with shorted probe.

I made some searching on oscilloscopes and concluded that non-toy scope starts at about $200.  There are three companies wort consideration: Siglent, Rigol (about the same) and Owon or Uni-T at the lower end.  Cheapest you can get is Hanmatek exact copy of Owon, but it is unknown brand, scope has two channels but no external trigger (deal breaker) and no test/calibration points (deal breaker as well).  This 100MHz Hanmatek would cost about $230 ending up $250 total, including tax.  Rigol has special at $299 (free shipping, no tax) on 2-channel scope, that they normally sell for $369.  It is DS1202Z-E  - a 2 channel 200MHz scope with 1Gs/s.  Of course 1Gs/s for 200MHz bandwidth is not enough but still, 200MHz is more transparent, rise time is 1.75ns and the probes are 350MHz.  This scope also includes free options worth probably as much as scope itself - Advance triggering, Memory depth upgrade, Real Time Waveform Record/Relay and Serial Bus Analysis.  It has only two channels but 4 channel scope is $50 more for 50MHz only.  Either scope is good choice, but I used to work with 100MHz 2GS/s two channel Agilent, that was sufficient most of the time.  In addition Rigol now gives warranty extension from 3 to 5 years for direct buys (or authorized dealers).  I bought this scope and just finished playing with it.  It is wonderful, well build instrument on the par with $1k Agilent.  It is very intuitive, in spite of tons of options, and has immaculate user's guide in pdf (plus other guides).  Of course I don't have to have it, but it was my tool at work and I feel I need to have it (bucket list).  Unfortunately the cheapest protective case that makes sense (size and quality) is one made by Rigol that is $58 at Newegg.  I bought it as well.

@jaytor  2-channel 200MHz scope is still 200MHz per channel.  Sampling rate drops by half but analog amplifiers are still 200MHz.  Some scopes (including mentioned Hanmatek) don't even drop sampling rate (dual A/D converter).