Speakers for Computer

There are models with a DAC and amplifier built in to the speakers and a large variety of inputs including wireless, ethernet USB, coax, toslink.
Here are a couple examples, not that I have a personal opinion about them: 

https://audioengineusa.com/shop/wirelessspeakers/a2-wireless-computer-speakers/

https://us.kef.com/ls50-wireless-2.html

My computer system includes a Hegel H160 integrated amp/DAC. My computer is connected to the H160 by a USB cable, so no sound card.  Lots of options. Good luck.  

Maybe consider looking at pro audio stores.  They have a wide variety of powered desktop monitors with analog and digital PC interfaces.

Digital or USB is best as it avoids any questions of the quality of components and noise in a PC's built in audio.

Computer into Small Sound System.

I spend a lot of time in my office. Last year I revised the whole room, files, desk, bc, and added a small sound system: real bookshelf speakers (fit on 11" deep shelf in a bookcase, seated ear level, no rear port), and 1 self-powered sub. Sub adds without awareness until you turn it off. It's a very enjoyable sound system. Nothing special, vintage B&W speakers from eBay, an old sub I had, a SS Carver Cube I had hanging around ....

You are closer to the heat in a smaller room, so don't overpower it. I'm gonna put a 2nd tube system for the TT and R2R, but the computer is staying low heat SS. Carver's are very low heat. And, I have a very quiet ceiling exhaust fan, for when I use the tubes.

I simply run the Computer’s sound out into the system. Stream, CD player built-in, copy cd's ...

Chair and monitor dead center of speakers, terrific sound and imaging. In my case I also have TT and R2R, you might think now about future additions.

Very happy with AudioEngine A5+, connected with Halide HD DAC from computer...

You only need a sound card for web recording. You DO need a USB DAC unless you enjoy crap sound and then you are in the wrong forum.
No recommendations for speakers, insufficient info.
Start with how loud you listen, how many $$ you wanna blow & how much size you have room for.