A lot of amplifiers are reviewed & measured
here on ASR.
I'm not afraid of budget amps with good speakers. Unlike speakers, most amps are better than human hearing so the main "spec" to look at is power. The Ascilab speakers are rated up to 250W but you probably don't "need" that much power in a regular home environment.
Sometimes there is audible noise (hum, hiss, or whine in the background). But the manufacturer's specs are useless because there's more than one way to measure noise. The measurements here are comparable but you can't always know if it's audible because it depends on the sensitivity of your speakers, how close you are to the speakers, and other ambient noise in the room. (Some "pro" amplifiers have cooling fans that make acoustic noise and that bothers some people.)
BTW - You can't trust manufacturer's wattage specs either. Most manufacturers seem to "fudge" a little, or a lot.
For 5.1 you should consider an AVR (audio video receiver). That's the most common and most practical way to do it. Unless a computer is your only source and then you can use a 5.1 channel soundcard. With an AVR you may not even need a separate amplifier, and if you intend to use separate amplifiers you need an AVR with "preamp outputs".
You need a way to decode the surround sound and with small speakers you need "bass management" to re-route the bass from the other channels to the subwoofer. An AVR does those things. I use an AVR and the only reason I have a separate amp is because I have a slightly non-standard setup with passive subwoofers.