Quantum Link, or Q-Link, was an early online service that evolved into AOL. Q-Link had a special graphical client for Commodore 64 that you had to use to connect, so it wasn't impossible to use at 300 bps. But you'd be waiting a long time to read even short posts at 30 bytes/s.
Then came 9600 bps, but there were a lot of incompatible standards (MNP-5, U.S. Robotics):
https://en.wikipedia.org/wiki/Microcom_Networking_Protocol
https://en.wikipedia.org/wiki/USRobotics
BBS's would advertise which brand of modem they had to get >2400 bps speeds.