Apologies, but STX didn't mean much to me in your OP because I'm more of a Hi-Fi and AV audio person than a PC audio one. Now you've given it the full name I have a better understanding of your equipment.
So, with the Asus Essence STX you could go either phono out or optical.
The reason for suggesting an AV amp was simply based on a set of presumptions built-up from dealing with lots of similar enquiries. You've been given some speakers at no cost; there's no budget set out in your OP; your background is PC rather than Hi-Fi/AV audio so your price expectations are probably based on PC speaker prices rather than AV/Hi-Fi; and it's likely that you want to get up and running at minimal cost (initially, at least) and yet cover as many bases as possible, which then may include adding or connecting other items to the system such as a TV or possibly a Sky or Freeview recorder box; and perhaps you're looking for something with the convenience of remote control? An AV Receiver ticks more of those boxes as a 'one stop' solution than does a Hi-Fi amp. Finally, although better than many PC speakers, the Technics SBC350's aren't really a Hi-Fi class speaker, so they're a performance bottleneck in terms of how much difference in audio quality you'll hear between different kinds of amps. Was any of that wildly off the mark?
I remember selling similar Technics speakers with their stack systems back in the mid-80's. Quite often the buyer would ask if there was any way to improve a system at the point of purchase. The answer was a speaker upgrade to a pair of Mission 70mkII Hi-Fi speakers @ £99. We sold very few Technics speakers and lots of Missions as a result.
In purist terms a Hi-Fi amp would be better, and for around the sort of money I've mentioned for a 2000+ vintage AV receiver you could pick up an 80's proper British Hi-Fi amp (Arcam, Creek, NAD, Rotel) as long as you're not too fussy about condition. If looking at something more recent then a 90's or early 2000's Cambridge Audio, Denon or possibly Marantz amp might just sneak in under the radar. Very few if any of these will have remote control for when you're sitting back just listening to music.
You might be tempted by the cheap T-amps advertised on Ebay. They're new of course, but of only limited real power output. The Technics speakers aren't that efficient, so like a fair bit of power behind them to get things moving. That would highlight the T-amp's Achilles heel.
As for AV receivers, there's been a massive amount of churn in the market with the development and adoption of new features such HDMI, 7.1, network streaming, app control etc. Then there's the Titanic price erosion as new models come out at ever lower prices. This pushes down secondhand prices to silly levels. There are some very capable older (pre-HDMI) receivers going for silly cheap money. Big Yamahas, Pioneers and Denons are particularly good value if all you need is basic stereo and AV features. These would have been anything from £800-£1500 new and pretty much top of the tree in terms of performance at the time they came out. For pure audio quality they'll even whup the butts of the modern £1000 AV receivers. This is because of the sonic arms race going on in the mid 2000's. HDMI hadn't yet hit and Blu-ray wouldn't launch officially until 2006, so at the time the manufacturers were heavily focussed on the sound quality battle. That probably marks the pinnacle of the power amp-side of design and build quality.
If you'd like to provide some more detail about your needs and budget then it might be possible to fine tune some recommendations.
