My first modem used was the 2400 baud internal in my PS/1 386SX. I eventually upgraded from that computer to a 486DX, which I hammered various upgrades into to make it a 486DX4. That had a 9800 baud fax modem, and I thought I was the shit for being able to send/receive faxes
I think that first modem I actually bought was a 14.4 for that computer's end of days period, and then I bought a Pentium 90. Things get fuzzy here...I know I upgraded...I think I went the 28.8 and stopped for a long time, before convincing my wife that we needed to spend the cash on a 56k.
Oh yes, things were rocking at that point!
After that was my Cisco ADSL modem, and then the cable modem.