Okay, since we're not talking about the BBS period in the 1980s, I'll skip that....
First time on the Internet was through a University account. I used Gopher a lot (as this was pre-WWW). I would dial into the University's VAX with my Amiga500 using JrTerm and a 2400 baud Supra modem (no, not 28K, 2400 - but I started on a 300 baud modem in the 1980s).
One of the first things I did was e-mail a guy in Washington for some reason (I live in central Canada). He replied while I was still in that particular session and I couldn't believe that I had gotten a written reply from across the continent almost immediately.
I remember reading the rumour - and then the confirmation - of the Commodore bankruptcy on the Usenet with this machine!