Take something like this Sceptre monitor, has built-in speakers.
If you can go with the 22" I'd root for it, but they have a 20" as well.
(For the built-in speaker to work you'll probably need to connect the computer to the monitor with the HDMI and not the VGA (does the computer have HDMI output?)
Ordered this, now I see in the box an HDMI cord and then a spot for the VGA cord, while I could get the screen to power on when connecting to the HDMI so used my old VGA and have the screen working, now I don't have sound.
Looked in the comments, seems you can either use the HDMI which I'm not sure how that would work or 3.5mm Aux wire, which I'm not sure why they couldn't include it and why such a short wire to power the screen?
If youre using HDMI, go to the sound settings:
Windows:
Look for the speaker icon in the bottom right (by the clock)
Right-click it
Click output/speaker
Find the HDMI interface (usually will say the name of the unit)
Right click and set as default.
If not using HDMI:
You need a 3.5mm (AUX) cable. One end in the headphone jack from the pc (usually green) and the other end to the back of the monitor marked input.