If you want to drive speakers to any kind of reasonable volume you'll need amplification. Computer speakers are usually amplified. Home audio speakers usually are not (there are exceptions, of course, like google or amazon smart speakers).
Adding audio_pwm_mode=2 to config.txt will enable higher quality analog audio out of the Pi3's 3.5mm jack.
The Pi Zero has no analog audio out (digital audio outputs through the HDMI port), but it can be added with a few inexpensive components on the GPIO (you'll still need amplification for speakers).
Computer speakers are usually amplified, and are available in a wide variety of sizes, configurations and price points.
However, the suggestion from dustnbone of using a Bluetooth speaker would be the simplest. A portable Bluetooth speaker should work with any wireless Pi model (such as the Pi Zero W). It would already include a battery for power in a nice, portable enclosure. You could build your instrument however you wanted and just set the speaker down wherever it's convenient to use (doesn't need to be integrated).
Oh, and since a Bluetooth speaker would be useful with your phone and other devices, the "I won't spend $50 on a $35 computer" budget doesn't necessarily apply (justification, in case you find a more expensive one you really want).
My mind is like a browser. 27 tabs are open, 9 aren't responding,
lots of pop-ups...and where is that annoying music coming from?