Tracing back to what would be a defining moment in my life is the Atari XM-301 300 baud modem for the old Atari 8-bit systems. Of course I didn't know it at the time, but there was no turning back once I had called my first BBS and chatted with the SysOp. I would eventually run a BBS a few years later off a floppy disk on my Atari 1040ST, once I had my own phone line. I still remember our old main house line number in Rockford and the BBS phone number. I still have the US Robotics modem that ran the last version of my BBS, and it still works, and still has the 'Not for Resale' badge on it due to obtaining it through the BBS SysOp program way back when.
I ran a BBS (Paragon) on my Amiga 500 with a 2400 baud modem. I was considered a high-speed BBS at that time I longed for a US Robotics 9600, but at $1,000 at the time it was a bit out of my league being that I was only 14.
This was my first modem, I saved up any penny I could get back when I was 10 years old. I spent many a day connecting to the local Rochester, NY Atari BBSes (Thanks Bob Puff!). This thing hauled for the day.. had to leave it behind when I picked a 1200 baud.