This one is going to be long, just so you know... 
Scroll to second post for current state.
The Journey
So, only at the end of March 2018 I started with 3D printing. It was an article in the Make Magazine (Germany) that recommended the Anet A8 as an affordable printer that, with some tweaks - some of them for security others for quality - would make a decent printer for about 250 €.
I saw a teaser to that article a lot earlier and did not even consider 3D printing at that time but a friend of mine buying the magazine triggered me into diving in this new hobby. I chose the Anet A8 based on the knowledge that I primarily buy this printer to print upgrades for the printer itself. A self-contained hobby so to speak.
So I went ahead and ordered the printer from TomTop which had the best price at that time for a model that was already in the EU and supposed to have short(er) delivery time. While waiting for the machine I was watching hours and hours of video on YouTube about other people also using Anet A8 as well as 3D printing in general.
I also ordered some upgrades immediately to improve or (even more important) make the printer more secure from the start. I read and heard a lot about the weak connection of the heated bed where they only used 2 of 4 available connections and too thin wires, so I ordered additional pairs of pre-made connector pins as well as thick wires. I ordered a MOSFET to control the power to the bed as the connectors on Anet's mainboard were known to be totally underrated for this task. Also some insulation for the heated bed, Igus drylin bearings (the cheap ones), mirror tiles from Ikea to be used as a print surface and also GT2 belts - not the original Gates but still those with glass-fiber instead of the default steel-fiber belts that come with the Anet A8. I also wanted to order a much more rigid holder for the heated bed but it was out of stock as the shop that was recommended for all the parts by the Make Magazine did not inform the shop owner in advance and he suddenly was swamped with orders and had a hard time to keep supplies coming in.
So, I built my Anet A8 never in the fully original state as I never used the belts or the linear bearings that came with it. To my positive surprise Anet seem to have reacted on the several reports of houses burnt down due to the weak heated bed connections (or heater cartridges falling out of the hotend) and upgraded these cables to be much more appropriate. Still I added ferrules where necessary and added a second pair of 2.5mm² cables running from PSU to the MOSFET for feeding the bed.
I got everything setup according to some build-videos on YouTube as well as some recommendations from the Make article and first test print was of a much better quality than I would have expected after all I read and heard about this printer before. It was almost at the level that I had seen when folks posted their results at the end of all their improvements - and I got them from a nearly stock model. But I also had the luck that all of my smooth rods were perfectly straight and not bent as a lot of other people.
But no reason to stop there. 
Next steps then were to finally get the then available-again holder for the heated bed and get the heated bed to a proper 3-point leveling - Make already recommended 3-point leveling but they said to just leave one of the four corners without a screw which led to a lot of oscillation when the bed moved quite fast. The new holder for the bed also allowed me to change it from a 4-point fixing to a 3-point fixing on the smooth rods as Prusa i3 is using. At that time I also switched from spring-suspension to suspension made from silicon rubber.
Printed a lot of improvements for my printer such as belt tentioners, frame rigidifiers, holders to allow to screw the printer to a wooden plate it was sitting on, a shroud for the PSU, a holder to attach the MOSFET properly to the frame, filament guide, a cover for the filament release screw, another part cooling duct and so on - small stuff that most people print to improve their printers.
Of course I also read about the problem that Anet had just disabled thermal runaway protection in their flavor of Marlin that was running on the printer so the next important change was a switch to the latest version of Marlin and man, that was great. I have no idea why but the printer suddenly was less noisy in some situations. Where it was "playing a song" when doing circles before it now was not longer distinguishable from sounds it made when printing straight lines - but that was still much too loud.
Silence!
There were multiple reasons why my printer needed to be more silent. First of all my wife was complaining about the noise - and as she is home most of the time and prints mostly run throughout the day (when I am not at home) I can absolutely understand that she was annoyed.
So, I went on the journey of getting this printer more silent. Or actually my goal was to have the most silent printer possible at a given speed.
The Igus bearings already helped a lot from the start. But a Nema 17 damper that I installed on the Y motor (which I identified of being the loudest) did not make a noticeable difference.
WD-40 helped a lot on the lead screws of the Z motors with their brass nuts though. These were finally swapped against ones made from POM though that again significantly reduced the noise of this part of the machine.
Also replacing the hotend fan that made a terrible noise by a ultra-silent model was... worlds of difference. This fan was always on when the machine was powered and you could hear this thing screaming all through the house - even with the door closed. I have no clue how you can even build such a loud fan. 
After the change the machine was totally silent in stand-by with the new fan running at full blast. I can hardly hear it with my ear next to fan. That helped also a lot.
Another factor was putting it on a thick rubber mat that usually is used to put a washing machine on. That damped a lot of vibrations that were before going to the table it sits on - and that then acted as an amplifier.
Trinamic is Silent!
But it was rather clear to me that with the original mainboard and its cheap stepper drivers (I have no clue what they are actually using below these tiny heatsinks) there was no way of getting a really silent printer. I had seen some videos on TMC2130 conversions and one was particularly impressive where a (German) YouTuber moved his modified Anet A8 with the microphone next to the printer and it was barely audible and im comparison he moved a stock one across the room and it blew my ears. So OK, it had to be TMC2130 with stealthChop.
I started comparing various possibilities how to do that. RAMPS + TMC2130 step sticks seemed to be an appropriate solution. But then I found the new Einsy RAMBo that was used in Prusa i3 MK3. They had the TMC2130 as surface mounted directly to the board which was supposed to make them better thermically. Huh, looks cool and has the capability of power-loss-recovery. But it is quite expensive compared to RAMPS even with genuine TMC2130 and not those Chinese clones.
And then I stumbled across the Duet. I do not remember where or how I got there but, yeah, I have a tendency to buy the most expensive and best options for my hobbies - even if I never use the full potential of it. But then again this board only as TMC drivers that were capable of spreadCycle and no stealthChop. Would this be silent enough? Argh, but it has 32-bit CPU... and... it... is... just... too... cool... to... not... buy... it.
You know how this ended since I am writing this at the Duet forum. Of course I went for the Duet and I never had the slightest amount of regret about it so far.
And, yeah, I have no idea how much quieter my printer would be if I would also have access to stealthChop but it is already so quiet with only spreadCycle and 256x microstepping (interpolated) that most noise is coming from part cooling blower fan.
Now after this rather long introduction let's get to the hard facts.
