Not my first modem (that would have been the Vicmodem on the CBM Vic
20,) but probably the oldest one I put to actual use was an
Andersen-Jacobson 300 baud model. It has disappeared into the maze of
junk in my basement so I don't have the full spec on it. But it was
direct connect, had heavy-duty toggles on the front and a classy
woodgrain veneer on the top and sides :)
Believe it or not I used it from about 1993-1995, in the leaner days
when a lot of my gear came from the dumpster at the local community
college.