https://www.amazon.co.uk/Syba-24-Bit-96KHz-Headphone-Amplifier/dp/B009WN7QT4 Is recommended by Zeos as "does the job".
The Syba sonic, is a headphone amp not a speaker amp. Hardyxd got a bit mixed up. Possibly missed the part where you mentioned about speakers.
SMSL SA36 or 50, maj mentioned, is a good choice for cheap small speaker amp.
There are some decent active speakers to be had, such as those from Edifier, if you'd prefer to go that route. They are very good, but one advantage to buying passive speakers and an amp, is that you can get many passive speakers that cost less than they used to. Active speakers don't drop in price the same way.
Also passive speakers are more solid in terms of reliability. As they have no amp inside, they have less electronics. Electronics will be the thing that go in active speakers, if there is an issue. With cheaper active speakers, more corners are cut to meet a price point. Very often that is that power supply. If it ever comes to it; cheaper to replace the amp, than the speakers.
Depending on what size of speaker you want and how much you want to spend, Wharfedale Diamond 9.0 are great speakers for around £50 from Richer Sounds.
Glad to help. I use a similar set up myself. I have a Topping TP21 amp and Roth Oli speakers. They are the same size as the Wharfedale's and for my desk, just right. Anything larger would be too big!
Did you go for desk speaker stands or floor standing ones?
Just curious, as some people do use desk stands to raise the speakers so the tweeter is ear height, and to help decouple the speakers from the desk to stop unwanted vibrations.
I put my amp's into standby mode, or at least soft off. The reason is it's kinder to electronics as it reduces the repeated surge of main power off/on over time.
Regarding warm up, yes you can get a change in sound, normally amps sound better after 20mins or so off use. You'll be hard pressed to notice the warm up on a modern class B amplifier, however I still believe it's there.
That setup looks really good, love the way you have positioned the amp.
Also very good you got your speakers on stands and isolated, makes a big difference. I would experiment with getting them away from wall more, just an extra 1-2cm can make a difference to sound.
Just a small tip, don't drive your speakers to hard at first, all speakers need some running in time, start at low volume then slowly play tracks louder, normally takes at least 20 hours of playing.
Is the click coming from the amp itself, is there any music/sound from the speakers before the click? If so it's probably normal, amp's have short circuit protection and as there is no short detected it's opening the circuit to the speakers.
It's strange that the click is happening with volume. I would have expected the click to open happen when the unit was switched on or off.
What I would do, play some music from the computer while turning the volume down, and see if the click suddenly cuts all sound from speakers.
It's probably the short circuit protection then. Again i'm no expert here, however what I believe is happening the amp is checking the impedance of speaker circuit, if there is no short detected, then the click is activating the output stage of amp. Providing the click is not happening when playing music (only happening when amp is turned on or off) I would not worry about it.