Sadly, I remember downloading porn off Commodore BBS’s. Some of it was dot shaded like “real” graphics and some of it was ASCII converted stuff. Not just ASCII drawings but photos converted by a program into an ASCII picture that you kind of have to step back from and squint a little.
Hey, you took what you could get.
I got my first computer with an acoustic modem in 1982. I was writing a book jointly with someone in Cleveland. Our computer centre arranged that my coauthor could connect to my account through something called Tymenet in the US and Datapac in Canada and we exchanged files that way. But that wasn’t the Internet. Then my son went off to Princeton in 1984 and discovered email. His self-help job was as a late-night consultant in the computing center. McGill was actually connected to the Internet but only the computer centre here had email. Every night my son sent an email to the computer centre asking why they didn’t have email for the whole university. Finally, in November, they did and we started exchanging emails regularly. So my email goes back to November of 1984.
Amusing followup. In the summer of 1985, my son got a summer job at the McGill computer centre. They told him that he was the #1 source of email to McGill from outside of Canada.
I started using email around 1989. I don’t remember using the internet before then.
I think I may have had an email address in college (91-95), but I didn’t have a computer and don’t remember using email much at all. My first job after college was at a tiny, small town newspaper that didn’t use the internet. At my next job, starting early '97, I had internet access at work and started using email (and reading the SDMB) regularly, though I didn’t have a computer at home. Now I work in social media.
I was using Telnet back in the late '70s as well, prolly 1978 or 1979 but as you say, it wasn’t exactly “the internet” back then. Still, there were systems online and as far as I was concerned, that meant there were systems that needed me to hack into them. 
I don’t remember, although I know the 1995-1996 window is at least true, so I answered that. Quite possibly the first category. We started using Telnet to access the local library through Gopher (that means text only in one-color and black glory). We also made do with month trials of Prodigy, Compuserve, etc. Either had to get disconnected when someone called, or block all incoming calls, because we only had one line. My dad was cheap.
We has an inkjet, and the monitor was only 16 or 256 colors, so it was better to just print porn.
Technically 1991 since I was using newsgroups and made literally one or two Internet emails that year.
I got my first internet based e-mail address in 1992. Used to hang out on some usenet groups and such back then. I did the BBS thing before that, but, as mentioned above, that doesn’t really count.
I remember using lynx for web browsing. And gopher for searches.
When the graphical web was young, I created a web page for one of my college’s minor sports. It was listed in a book that claimed to be the canonical list of all web pages. I wish I had a copy of it. 
I also remember the first time I heard about the graphical web - a VJ on MTV made a reference to it. Back in the NCSA Mosaic days.
Trivial uses back in 1979 when I started college (I was a computer science major) - stuff like playing games and sending emails.
First real access was when I bought my first computer back in 1991 and I was accessing BBS’s with my 1200 baud modem.
1995-1996
In April 1996 I went to work for E*Trade. Before that I didn’t have internet access at home, but we did have it at the TV station I was working at before that and we had email there.
Hey! I just found out they shut down Bianca’s Smut Shack!
Okay, they shut it down in 2001. But I should have been notified.
I don’t know about '79, but when I was on PLATO from '74-77 everything was run off of the two CDC machines at Illinois. Those far away using it still were on those machines. However we had much of what the web has now, including email, chatrooms, instant messaging, message boards, MUDs and other interactive games, and a newspaper. And even a very limited pornish lesson.
It was sometime in the mid-90’s, I really don’t remember the year. I remember not minding dial-up because of course no one knew any better yet, something about disabling call waiting while online, and leaving my desk to do small tasks, make coffee or tea, stuff like that while pages loaded.
The real test whether you’ve been on the net a long time is if you were sending email before domain addressing - that is, when you had to specify the path from your computer to the destination, which means you remember the backbone servers - ihnp4, decvax, ucbvax. In fact, you really had to know the names of computers.
I was doing this soon after 1980. I was on the Arpanet in '74 when we used it from Illinois to play the Parry simulation at Stanford. But that’s not quite the internet yet.
I got a free shell account while in College in 1993 or so. Used it for e-mail and to read tons of Usenet (including the Usenet Straight Dope group). Also played around with FTP and Gopher.
Stuck with a shell account after graduating. Used a small provider (remember them?) who didn’t even have a local number for me (I ran up huge phone bills). Switched over to Netcom to get a normal internet account that could use the Web. Netcom got bought by Mindspring which got bought by Earthlink which I still use to this day. My e-mail still has a Netcom domain but not plain Netcom.com since at the time I joined those were for people that stuck with Netcom’s shell accounts.
I remember staking out the “good” computer in the lab that could do BOTH word processing AND surf the web with Netscape back in 94, 95.
How annoyed I was when websites started adding pictures and all I used at home was lynx.
Starting using BBS’s on 300 baud around '85. Ran my own board from 95 to 99.
Archie. Archie searches. To find gopher sites. sigh
Ooh. UUCP bang paths! I actually ran into them briefly in the late 80s, but not in a serious enough way that I count it as using the 'net.
Way back in the day, I took a computer course in high school, 1970, where we connected by telephone modem to a computer somewhere?? in Illinois. Next interwebs was in the early 80’s.
aarnet of course was around back then, I started on the internet in 1992 but I was working for Telecom Australia at the time and sold data lines.