For me, the three most classic bass guitar designs (and tones) come from the Fender Jazz, Fender Precision, and MusicMan StingRay.
It's probably no coincidence that Leo Fender had a huge say in all three basses...
In this bass guitar tutorial, listen to the tones from a 1978 MusicMan StingRay as well as a more modern StingRay 5.
They're more versatile than you might think.
In the video, I mentioned an amazing Pino Palladino fretless performance. Here it is:
Fender Jazz & Precision Bass Guitar Tones
If you enjoyed that rundown, make sure to watch the ones I did on the Fender Jazz and Precision basses.