Well I am no expert oscilloscope reviewer, and this is what I have found out so far:
1) Low voltage signals are affected by all the noise sources inside the scope as mentioned in the pages above,
anything below +/-0.5V pk is problematic.
This problem is in your Owon becouse you are one who have this most bad noisy GND issue.
Here is some pictures from factory new Owons and mesurments made so that it really show worst. Oscilloscope run with mains power (not with battery)
Probe connected to signal with its own GND wire with alligator. Oscilloscope is in normal enviroment and signal source is also connected to mains power.
Scope and signal source are so that common mode noise picked up from equipments itself and from enviroment is as bad as it is typically and also connected to laptop so that situation is as bad as can be if think what kind of "antenna" this whole test setup is.
20mVpp do not look very problematic. There is connection with normal GND wire and then with short GND spring what is very normal practice if people have any real experience about measurements and for avoid problems.
(also it is very good to look this youtube from Dave where he hanging around Rigol DS2202 and common mode noise.
Look what happend there related to Rigol TFT. (yes Owon do same)
Look carefully. There is some very "fun" details.
Specially starting after 13.30. (TFT)
Also 17.38 is short very interesting point. Coaxial cable near Rigol TFT.
But these pictures attached show how it is here and related problems under +/-0.5Vpp signals as you tell. My opinion is that it is not very problematic. And methods and settings I use for these are just these "entry level" practices where all conncted as "magpie nest".
Some reader may see more and some may see less problems.
2) MATHS and MEASUREMENT seems to work from what is displayed on the screen. It seems that the scope has two
memory areas: one is what it captures (raw data) and he second memory area is what it displays on the screen.
Maths and measurements are derived from the screen data, it seems, which is a very bad idea. Quick example: take
two sinusoidal signals, one is 50V pk, the other is 48V pk. The difference is 2V pk, and this is what the MATHS
will display. However this 2V curve is almost a flat line when you are also displaying a 50V, ie the division is
10V. There is nothing you can do to "zoom in" on the MATHs curve, because this will take the other two curves out
of range and you will get garbage on the screen.
There is 2pcs
8bit (*1) ADC's
((*1) and then note all things in practice what reduce conversion result quality)
It is good to understand this simple math.
Data for math is 8bit. What happend if in one point result is 120-120 and then next place 122 - 120.
Difference between these is 2. There is 4 pixels vertically. Yes you can zoom it. Where is now more information if you have nearly half div for one resolution step. Zoom can not add resolution!
For my eyes some times zoom factor 2 or 4 is enough for better visibility if difference is quite small. (btw. how it differ in vertical direction from raw vector data in practice?)
In picture I have zoomed by 10x (inputs 2V/div and math 200mV/div)
It is different case if we have more resolution than 8bit and then we have lot of less resolution in display. Now our display resolution is more (double) than data resolution.
Look these example pictures.
3) fan makes constant and annoying noise - wondering if it could be variable speed like on my laptop :-)
Do you know what this price class oscilloscope have more silent fan? If there is fan.
I know one. Siglent but difference is very marginal.
But in other hand, time ago Owon have some extra problems with fans. Many fans was assembled wrong and / or damaged in assembly in factory and after short time or just new from package make very very bad noise.
These fans need change.
Pictures (picture names give some explanation also)
First 2 pictures for this Math "zoom"
and then some pictures related to: "anything below +/-0.5V pk is problematic."
In some pictures these is Acquire mode PEAK. If filename read acqN there is Normal mode.