@elrainia@lemmy.world describes working on internet infrastructure back in the 1990s. This was on one of those "drive by" AskLemmys where a new user posts a juicy question, then after a couple hours they delete the topic and their account. However, those posts and comments are still visible in Piefed, ex: https://piefed.social/post/1733969#comment_9969293
You're more or less right, 9600bps modems did exist in the late 80s, but no mere mortal owned them 14.4k came not long after and became really common. I actually saved up and got one of the first 19.2k modems on the market when I was a teen in 93 or so, but almost nothing was compatible with it so it was usually just 14.4k or 9600 if you tried to connect to anything.
Technically, its gets weird because in the late 80s baud and bits per second kind of diverged because of the way the protocols were able to encode data better. I don't think anything actually went higher than 2400 baud though we kept using baud and bps interchangeably.