I personally use the Klipsch Promedia 2.1 computer speaker set. These are quite famous for being the best speakers you could get that were targeted/designed to be hooked upto a computer machine. I've had them for about 12 years or more, still work amazing and I've had 6 different people over hear them and listen in for a bit, in turn all of them went out and bought themselves a set as well.
They look great, small profile but made of very heavy solid plastic and they heavier then expected when picked up. I believe they are ~30 watt RMS each, with 3" long throw speakers cones and 3/4" Horned Tweeters each. It comes with well built, ported 6 1/2" 150watt wooden sub.
For amplified computer speakers I have never heard better, to get better quality you are going to have to go with the amplified reciever/bookshelf speaker set-up.
Goodnews is, is that Klipsh still sells them new to this day. But be aware this set is cheaper and by the reviews seems they don't sound identicle to the originals. But if you don't want to spend more then 150$ these should hit the sweet spot.
https://www.amazon.com/Klipsch-ProMedia-Certified-Computer-S...
A good set of book shelf speakers or studio monitors are probably what you're looking for. Careful how much you spend because if you've never had quality audio equipment before you might find yourself with an expensive new hobby.
My normal desktop setup is an Indeed class D amplifier powering a pair of Emotiva XRM-4.1 monitoring speakers, connected to an Asus Xonar sound card. The speakers are great but I'd like to upgrade the amp and add a dedicated DAC in the future. I've also had a great experience with Emotiva's Airmotiv line for home theater applications.
If i was going to run it to an amp I'd probably run it via a long jack, there are these fancy wireless things available these days for a couple of bucks but meh, good old wires for the win.