It was a Radio Shack 300 baud modem. A little googling seems to indicate is would likely have been a Tandy DCM-3 “Direct Connect” (as opposed to acoustic coupler) modem.
It was in-line between the wall and a phone so you would pick up the phone, dial the number, head the modem tone, press a red button on the top of the modem and hang up the phone.
My very first experience with Linux was in probably 1993 or so. I ran a dial-up BBS with a Usenet feed and a friend UUCP'd me the first few floppies of slackware to try. I don't remember getting very far but I had used OS/9 earlier on my Coco 3, so the shell was pretty familiar.
For actual work, about a year later I started working for a dial-up ISP and my workstation was a Linux box connected via Serial PPP to a Sun pizzabox.
I've used Linux on and off as a Desktop over the years but always maintained at least one server. In my current jobs there is a mix of Linux and FreeBSD servers I run on a Linux based virtualization platform.